diff --git a/src/ControlSystem/Actions/LimitTimeStep.hpp b/src/ControlSystem/Actions/LimitTimeStep.hpp
index 2e31d4c09e2e..f2917987c7ee 100644
--- a/src/ControlSystem/Actions/LimitTimeStep.hpp
+++ b/src/ControlSystem/Actions/LimitTimeStep.hpp
@@ -16,7 +16,6 @@
 #include "Parallel/GlobalCache.hpp"
 #include "Time/ChangeSlabSize.hpp"
 #include "Time/Tags/HistoryEvolvedVariables.hpp"
-#include "Time/Tags/TimeStepper.hpp"
 #include "Utilities/ErrorHandling/Assert.hpp"
 #include "Utilities/ErrorHandling/Error.hpp"
 #include "Utilities/Gsl.hpp"
@@ -26,7 +25,10 @@
 namespace Tags {
 struct TimeStep;
 struct TimeStepId;
+template <typename StepperInterface>
+struct TimeStepper;
 }  // namespace Tags
+class TimeStepper;
 namespace control_system::Tags {
 template <typename ControlSystems>
 struct FutureMeasurements;
@@ -93,7 +95,7 @@ struct LimitTimeStep {
       return {Parallel::AlgorithmExecution::Continue, std::nullopt};
     }
 
-    const auto& time_stepper = db::get<::Tags::TimeStepper<>>(box);
+    const auto& time_stepper = db::get<::Tags::TimeStepper<TimeStepper>>(box);
     if (time_stepper.number_of_substeps() == 1) {
       // If there are no substeps, there is no reason to limit the
       // step size so substeps can be evaluated.  Single-substep FSAL
diff --git a/src/Evolution/Actions/RunEventsAndDenseTriggers.hpp b/src/Evolution/Actions/RunEventsAndDenseTriggers.hpp
index a935ac92a852..4ef98611abb3 100644
--- a/src/Evolution/Actions/RunEventsAndDenseTriggers.hpp
+++ b/src/Evolution/Actions/RunEventsAndDenseTriggers.hpp
@@ -18,7 +18,6 @@
 #include "Time/EvolutionOrdering.hpp"
 #include "Time/Tags/HistoryEvolvedVariables.hpp"
 #include "Time/Tags/Time.hpp"
-#include "Time/Tags/TimeStepper.hpp"
 #include "Time/TimeSteppers/TimeStepper.hpp"
 #include "Utilities/Gsl.hpp"
 #include "Utilities/TMPL.hpp"
@@ -41,6 +40,8 @@ class GlobalCache;
 namespace Tags {
 struct TimeStep;
 struct TimeStepId;
+template <typename StepperInterface>
+struct TimeStepper;
 }  // namespace Tags
 /// \endcond
 
@@ -269,7 +270,8 @@ struct RunEventsAndDenseTriggers {
                 dense_output_succeeded =
                     stepper.dense_update_u(vars, history, next_trigger);
               },
-              make_not_null(&box), db::get<::Tags::TimeStepper<>>(box),
+              make_not_null(&box),
+              db::get<::Tags::TimeStepper<TimeStepper>>(box),
               db::get<history_tag>(box));
           if (not dense_output_succeeded) {
             // Need to take another time step
diff --git a/src/Evolution/DgSubcell/Actions/TciAndSwitchToDg.hpp b/src/Evolution/DgSubcell/Actions/TciAndSwitchToDg.hpp
index 41d30c013ac1..fd508004c8e4 100644
--- a/src/Evolution/DgSubcell/Actions/TciAndSwitchToDg.hpp
+++ b/src/Evolution/DgSubcell/Actions/TciAndSwitchToDg.hpp
@@ -37,7 +37,6 @@
 #include "Parallel/AlgorithmExecution.hpp"
 #include "Time/History.hpp"
 #include "Time/Tags/HistoryEvolvedVariables.hpp"
-#include "Time/Tags/TimeStepper.hpp"
 #include "Time/TimeStepId.hpp"
 #include "Utilities/ContainerHelpers.hpp"
 #include "Utilities/ErrorHandling/Assert.hpp"
@@ -51,7 +50,10 @@ class GlobalCache;
 }  // namespace Parallel
 namespace Tags {
 struct TimeStepId;
+template <typename StepperInterface>
+struct TimeStepper;
 }  // namespace Tags
+class TimeStepper;
 namespace tuples {
 template <typename...>
 class TaggedTuple;
@@ -246,7 +248,7 @@ struct TciAndSwitchToDg {
     //              the entire TCI history is `ActiveGrid::Dg`.
     // - Substep: the easiest is to restrict switching back to DG to step
     //            boundaries where there is no history.
-    const auto& time_stepper = db::get<::Tags::TimeStepper<>>(box);
+    const auto& time_stepper = db::get<::Tags::TimeStepper<TimeStepper>>(box);
     const bool is_substep_method = time_stepper.number_of_substeps() != 1;
     ASSERT(time_stepper.number_of_substeps() != 0,
            "Don't know how to handle a time stepper with zero substeps. This "
diff --git a/src/Evolution/DiscontinuousGalerkin/Actions/ApplyBoundaryCorrections.hpp b/src/Evolution/DiscontinuousGalerkin/Actions/ApplyBoundaryCorrections.hpp
index f5a1e161b4ec..09460d5f93a3 100644
--- a/src/Evolution/DiscontinuousGalerkin/Actions/ApplyBoundaryCorrections.hpp
+++ b/src/Evolution/DiscontinuousGalerkin/Actions/ApplyBoundaryCorrections.hpp
@@ -41,7 +41,6 @@
 #include "Parallel/GlobalCache.hpp"
 #include "Time/BoundaryHistory.hpp"
 #include "Time/EvolutionOrdering.hpp"
-#include "Time/Tags/TimeStepper.hpp"
 #include "Time/Time.hpp"
 #include "Time/TimeStepId.hpp"
 #include "Time/TimeSteppers/LtsTimeStepper.hpp"
@@ -59,6 +58,8 @@ namespace Tags {
 struct Time;
 struct TimeStep;
 struct TimeStepId;
+template <typename StepperInterface>
+struct TimeStepper;
 }  // namespace Tags
 /// \endcond
 
@@ -361,7 +362,8 @@ struct ApplyBoundaryCorrections {
       domain::Tags::Mesh<volume_dim>, Tags::MortarMesh<volume_dim>,
       Tags::MortarSize<volume_dim>, ::dg::Tags::Formulation,
       evolution::dg::Tags::NormalCovectorAndMagnitude<volume_dim>,
-      ::Tags::TimeStepper<>, evolution::Tags::BoundaryCorrection<system>,
+      ::Tags::TimeStepper<TimeStepperType>,
+      evolution::Tags::BoundaryCorrection<system>,
       tmpl::conditional_t<DenseOutput, ::Tags::Time, ::Tags::TimeStep>,
       tmpl::conditional_t<local_time_stepping, tmpl::list<>,
                           domain::Tags::DetInvJacobian<Frame::ElementLogical,
diff --git a/src/Evolution/Executables/Burgers/EvolveBurgers.hpp b/src/Evolution/Executables/Burgers/EvolveBurgers.hpp
index 2665b4bf7d9b..e434ffaab0ae 100644
--- a/src/Evolution/Executables/Burgers/EvolveBurgers.hpp
+++ b/src/Evolution/Executables/Burgers/EvolveBurgers.hpp
@@ -120,7 +120,10 @@ struct EvolutionMetavars {
   static constexpr size_t volume_dim = 1;
   using system = Burgers::System;
   using temporal_id = Tags::TimeStepId;
-  static constexpr bool local_time_stepping = false;
+  using TimeStepperBase = TimeStepper;
+
+  static constexpr bool local_time_stepping =
+      TimeStepperBase::local_time_stepping;
 
   // The use_dg_subcell flag controls whether to use "standard" limiting (false)
   // or a DG-FD hybrid scheme (true).
@@ -281,7 +284,7 @@ struct EvolutionMetavars {
 
   using initialization_actions = tmpl::list<
       Initialization::Actions::InitializeItems<
-          Initialization::TimeStepping<EvolutionMetavars, local_time_stepping>,
+          Initialization::TimeStepping<EvolutionMetavars, TimeStepperBase>,
           evolution::dg::Initialization::Domain<1>,
           Initialization::TimeStepperHistory<EvolutionMetavars>>,
       Initialization::Actions::ConservativeSystem<system>,
diff --git a/src/Evolution/Executables/CurvedScalarWave/EvolveCurvedScalarWave.hpp b/src/Evolution/Executables/CurvedScalarWave/EvolveCurvedScalarWave.hpp
index 8c782ef41a31..6a459cd1e0dc 100644
--- a/src/Evolution/Executables/CurvedScalarWave/EvolveCurvedScalarWave.hpp
+++ b/src/Evolution/Executables/CurvedScalarWave/EvolveCurvedScalarWave.hpp
@@ -129,7 +129,10 @@ struct EvolutionMetavars {
 
   using system = CurvedScalarWave::System<Dim>;
   using temporal_id = Tags::TimeStepId;
-  static constexpr bool local_time_stepping = true;
+  using TimeStepperBase = LtsTimeStepper;
+
+  static constexpr bool local_time_stepping =
+      TimeStepperBase::local_time_stepping;
 
   using analytic_solution_fields = typename system::variables_tag::tags_list;
   using deriv_compute = ::Tags::DerivCompute<
@@ -271,7 +274,7 @@ struct EvolutionMetavars {
 
   using initialization_actions = tmpl::list<
       Initialization::Actions::InitializeItems<
-          Initialization::TimeStepping<EvolutionMetavars, local_time_stepping>,
+          Initialization::TimeStepping<EvolutionMetavars, TimeStepperBase>,
           evolution::dg::Initialization::Domain<volume_dim>,
           Initialization::TimeStepperHistory<EvolutionMetavars>>,
       Initialization::Actions::NonconservativeSystem<system>,
diff --git a/src/Evolution/Executables/CurvedScalarWave/EvolveWorldtubeCurvedScalarWave.hpp b/src/Evolution/Executables/CurvedScalarWave/EvolveWorldtubeCurvedScalarWave.hpp
index 103332bed308..0f9c4d8ff038 100644
--- a/src/Evolution/Executables/CurvedScalarWave/EvolveWorldtubeCurvedScalarWave.hpp
+++ b/src/Evolution/Executables/CurvedScalarWave/EvolveWorldtubeCurvedScalarWave.hpp
@@ -141,9 +141,11 @@ struct EvolutionMetavars {
 
   using system = CurvedScalarWave::System<volume_dim>;
   using temporal_id = Tags::TimeStepId;
+  // LTS not implemented yet
+  using TimeStepperBase = TimeStepper;
 
-  // not implemented yet
-  static constexpr bool local_time_stepping = false;
+  static constexpr bool local_time_stepping =
+      TimeStepperBase::local_time_stepping;
 
   using analytic_solution_fields = typename system::variables_tag::tags_list;
   using deriv_compute = ::Tags::DerivCompute<
@@ -274,7 +276,7 @@ struct EvolutionMetavars {
 
   using initialization_actions = tmpl::list<
       Initialization::Actions::InitializeItems<
-          Initialization::TimeStepping<EvolutionMetavars, local_time_stepping>,
+          Initialization::TimeStepping<EvolutionMetavars, TimeStepperBase>,
           evolution::dg::Initialization::Domain<volume_dim>,
           Initialization::TimeStepperHistory<EvolutionMetavars>>,
       Initialization::Actions::NonconservativeSystem<system>,
diff --git a/src/Evolution/Executables/ForceFree/EvolveForceFree.hpp b/src/Evolution/Executables/ForceFree/EvolveForceFree.hpp
index 82b8f87db450..359d0816e638 100644
--- a/src/Evolution/Executables/ForceFree/EvolveForceFree.hpp
+++ b/src/Evolution/Executables/ForceFree/EvolveForceFree.hpp
@@ -100,7 +100,10 @@ struct EvolutionMetavars {
   static constexpr size_t volume_dim = 3;
   using system = ForceFree::System;
   using temporal_id = Tags::TimeStepId;
-  static constexpr bool local_time_stepping = false;
+  using TimeStepperBase = TimeStepper;
+
+  static constexpr bool local_time_stepping =
+      TimeStepperBase::local_time_stepping;
 
   using initial_data_list = tmpl::append<ForceFree::Solutions::all_solutions,
                                          ForceFree::AnalyticData::all_data>;
@@ -201,7 +204,7 @@ struct EvolutionMetavars {
 
   using initialization_actions = tmpl::list<
       Initialization::Actions::InitializeItems<
-          Initialization::TimeStepping<EvolutionMetavars, local_time_stepping>,
+          Initialization::TimeStepping<EvolutionMetavars, TimeStepperBase>,
           evolution::dg::Initialization::Domain<volume_dim>,
           Initialization::TimeStepperHistory<EvolutionMetavars>>,
       Initialization::Actions::AddSimpleTags<
diff --git a/src/Evolution/Executables/GeneralizedHarmonic/EvolveGhAndCharacteristic.hpp b/src/Evolution/Executables/GeneralizedHarmonic/EvolveGhAndCharacteristic.hpp
index 5566c703cad4..a72f95d8e857 100644
--- a/src/Evolution/Executables/GeneralizedHarmonic/EvolveGhAndCharacteristic.hpp
+++ b/src/Evolution/Executables/GeneralizedHarmonic/EvolveGhAndCharacteristic.hpp
@@ -74,6 +74,7 @@ struct EvolutionMetavars : public GeneralizedHarmonicTemplateBase<3>,
   using typename gh_base::initialize_initial_data_dependent_quantities_actions;
   using cce_boundary_component = Cce::GhWorldtubeBoundary<EvolutionMetavars>;
 
+  using TimeStepperBase = typename gh_base::TimeStepperBase;
   static constexpr bool local_time_stepping = gh_base::local_time_stepping;
 
   template <bool DuringSelfStart>
@@ -133,7 +134,7 @@ struct EvolutionMetavars : public GeneralizedHarmonicTemplateBase<3>,
   // addition of initializing the interpolation points (second-to-last action).
   using initialization_actions = tmpl::list<
       Initialization::Actions::InitializeItems<
-          Initialization::TimeStepping<EvolutionMetavars, local_time_stepping>,
+          Initialization::TimeStepping<EvolutionMetavars, TimeStepperBase>,
           evolution::dg::Initialization::Domain<volume_dim>,
           Initialization::TimeStepperHistory<EvolutionMetavars>>,
       Initialization::Actions::NonconservativeSystem<system>,
diff --git a/src/Evolution/Executables/GeneralizedHarmonic/EvolveGhBinaryBlackHole.hpp b/src/Evolution/Executables/GeneralizedHarmonic/EvolveGhBinaryBlackHole.hpp
index ce1460f183b8..097786a3415a 100644
--- a/src/Evolution/Executables/GeneralizedHarmonic/EvolveGhBinaryBlackHole.hpp
+++ b/src/Evolution/Executables/GeneralizedHarmonic/EvolveGhBinaryBlackHole.hpp
@@ -224,7 +224,10 @@ struct EvolutionMetavars {
   static constexpr dg::Formulation dg_formulation =
       dg::Formulation::StrongInertial;
   using temporal_id = Tags::TimeStepId;
-  static constexpr bool local_time_stepping = true;
+  using TimeStepperBase = LtsTimeStepper;
+
+  static constexpr bool local_time_stepping =
+      TimeStepperBase::local_time_stepping;
 
   using initialize_initial_data_dependent_quantities_actions = tmpl::list<
       Actions::MutateApply<gh::gauges::SetPiAndPhiFromConstraints<volume_dim>>,
@@ -529,7 +532,7 @@ struct EvolutionMetavars {
 
   using initialization_actions = tmpl::list<
       Initialization::Actions::InitializeItems<
-          Initialization::TimeStepping<EvolutionMetavars, local_time_stepping>,
+          Initialization::TimeStepping<EvolutionMetavars, TimeStepperBase>,
           evolution::dg::Initialization::Domain<volume_dim,
                                                 use_control_systems>,
           Initialization::TimeStepperHistory<EvolutionMetavars>>,
diff --git a/src/Evolution/Executables/GeneralizedHarmonic/GeneralizedHarmonicBase.hpp b/src/Evolution/Executables/GeneralizedHarmonic/GeneralizedHarmonicBase.hpp
index 352d6ce860ea..f8b1a6bc1fdf 100644
--- a/src/Evolution/Executables/GeneralizedHarmonic/GeneralizedHarmonicBase.hpp
+++ b/src/Evolution/Executables/GeneralizedHarmonic/GeneralizedHarmonicBase.hpp
@@ -295,7 +295,10 @@ template <size_t VolumeDim>
 struct GeneralizedHarmonicTemplateBase {
   static constexpr size_t volume_dim = VolumeDim;
   using system = gh::System<volume_dim>;
-  static constexpr bool local_time_stepping = false;
+  using TimeStepperBase = TimeStepper;
+
+  static constexpr bool local_time_stepping =
+      TimeStepperBase::local_time_stepping;
 
   // NOLINTNEXTLINE(google-runtime-references)
   void pup(PUP::er& /*p*/) {}
@@ -364,7 +367,7 @@ struct GeneralizedHarmonicTemplateBase {
   template <typename DerivedMetavars, bool UseControlSystems>
   using initialization_actions = tmpl::list<
       Initialization::Actions::InitializeItems<
-          Initialization::TimeStepping<DerivedMetavars, local_time_stepping>,
+          Initialization::TimeStepping<DerivedMetavars, TimeStepperBase>,
           evolution::dg::Initialization::Domain<volume_dim, UseControlSystems>,
           Initialization::TimeStepperHistory<DerivedMetavars>>,
       Initialization::Actions::NonconservativeSystem<system>,
diff --git a/src/Evolution/Executables/GrMhd/GhValenciaDivClean/GhValenciaDivCleanBase.hpp b/src/Evolution/Executables/GrMhd/GhValenciaDivClean/GhValenciaDivCleanBase.hpp
index 0dfe029b05f0..fc32d2f74fc3 100644
--- a/src/Evolution/Executables/GrMhd/GhValenciaDivClean/GhValenciaDivCleanBase.hpp
+++ b/src/Evolution/Executables/GrMhd/GhValenciaDivClean/GhValenciaDivCleanBase.hpp
@@ -260,7 +260,10 @@ struct GhValenciaDivCleanDefaults {
   using domain_frame = Frame::Inertial;
   static constexpr bool use_damped_harmonic_rollon = true;
   using temporal_id = Tags::TimeStepId;
-  static constexpr bool local_time_stepping = false;
+  using TimeStepperBase = TimeStepper;
+
+  static constexpr bool local_time_stepping =
+      TimeStepperBase::local_time_stepping;
 
   using system = grmhd::GhValenciaDivClean::System;
   using analytic_variables_tags =
@@ -347,6 +350,7 @@ struct GhValenciaDivCleanTemplateBase<
   static constexpr bool use_damped_harmonic_rollon =
       defaults::use_damped_harmonic_rollon;
   using temporal_id = typename defaults::temporal_id;
+  using TimeStepperBase = typename defaults::TimeStepperBase;
   static constexpr bool local_time_stepping = defaults::local_time_stepping;
   using system = typename defaults::system;
   using analytic_variables_tags = typename defaults::analytic_variables_tags;
@@ -783,7 +787,7 @@ struct GhValenciaDivCleanTemplateBase<
 
   using initialization_actions = tmpl::list<
       Initialization::Actions::InitializeItems<
-          Initialization::TimeStepping<derived_metavars, local_time_stepping>,
+          Initialization::TimeStepping<derived_metavars, TimeStepperBase>,
           evolution::dg::Initialization::Domain<3, use_control_systems>,
           Initialization::TimeStepperHistory<derived_metavars>>,
       Initialization::Actions::ConservativeSystem<system>,
diff --git a/src/Evolution/Executables/GrMhd/ValenciaDivClean/EvolveValenciaDivClean.hpp b/src/Evolution/Executables/GrMhd/ValenciaDivClean/EvolveValenciaDivClean.hpp
index e7b3388e1982..28404208b074 100644
--- a/src/Evolution/Executables/GrMhd/ValenciaDivClean/EvolveValenciaDivClean.hpp
+++ b/src/Evolution/Executables/GrMhd/ValenciaDivClean/EvolveValenciaDivClean.hpp
@@ -227,7 +227,11 @@ struct EvolutionMetavars<tmpl::list<InterpolationTargetTags...>,
   using initial_data_tag = evolution::initial_data::Tags::InitialData;
   using system = grmhd::ValenciaDivClean::System;
   using temporal_id = Tags::TimeStepId;
-  static constexpr bool local_time_stepping = false;
+  using TimeStepperBase = TimeStepper;
+
+  static constexpr bool local_time_stepping =
+      TimeStepperBase::local_time_stepping;
+
   using analytic_variables_tags =
       typename system::primitive_variables_tag::tags_list;
   using equation_of_state_tag = hydro::Tags::GrmhdEquationOfState;
@@ -506,7 +510,7 @@ struct EvolutionMetavars<tmpl::list<InterpolationTargetTags...>,
 
   using initialization_actions = tmpl::flatten<tmpl::list<
       Initialization::Actions::InitializeItems<
-          Initialization::TimeStepping<EvolutionMetavars, local_time_stepping>,
+          Initialization::TimeStepping<EvolutionMetavars, TimeStepperBase>,
           evolution::dg::Initialization::Domain<3>,
           Initialization::TimeStepperHistory<EvolutionMetavars>>,
       Initialization::Actions::AddSimpleTags<
diff --git a/src/Evolution/Executables/NewtonianEuler/EvolveNewtonianEuler.hpp b/src/Evolution/Executables/NewtonianEuler/EvolveNewtonianEuler.hpp
index 16408fe2793e..45a163aae86b 100644
--- a/src/Evolution/Executables/NewtonianEuler/EvolveNewtonianEuler.hpp
+++ b/src/Evolution/Executables/NewtonianEuler/EvolveNewtonianEuler.hpp
@@ -148,7 +148,10 @@ struct EvolutionMetavars {
   using system = NewtonianEuler::System<Dim, initial_data>;
 
   using temporal_id = Tags::TimeStepId;
-  static constexpr bool local_time_stepping = false;
+  using TimeStepperBase = TimeStepper;
+
+  static constexpr bool local_time_stepping =
+      TimeStepperBase::local_time_stepping;
 
   using initial_data_tag =
       tmpl::conditional_t<is_analytic_solution_v<initial_data>,
@@ -254,7 +257,7 @@ struct EvolutionMetavars {
 
   using initialization_actions = tmpl::flatten<tmpl::list<
       Initialization::Actions::InitializeItems<
-          Initialization::TimeStepping<EvolutionMetavars, local_time_stepping>,
+          Initialization::TimeStepping<EvolutionMetavars, TimeStepperBase>,
           evolution::dg::Initialization::Domain<Dim>,
           Initialization::TimeStepperHistory<EvolutionMetavars>>,
       Initialization::Actions::ConservativeSystem<system>,
diff --git a/src/Evolution/Executables/RadiationTransport/M1Grey/EvolveM1Grey.hpp b/src/Evolution/Executables/RadiationTransport/M1Grey/EvolveM1Grey.hpp
index 44662884293f..972d1fc3ca2b 100644
--- a/src/Evolution/Executables/RadiationTransport/M1Grey/EvolveM1Grey.hpp
+++ b/src/Evolution/Executables/RadiationTransport/M1Grey/EvolveM1Grey.hpp
@@ -117,7 +117,11 @@ struct EvolutionMetavars {
 
   using system = RadiationTransport::M1Grey::System<neutrino_species>;
   using temporal_id = Tags::TimeStepId;
-  static constexpr bool local_time_stepping = false;
+  using TimeStepperBase = TimeStepper;
+
+  static constexpr bool local_time_stepping =
+      TimeStepperBase::local_time_stepping;
+
   using initial_data_tag =
       tmpl::conditional_t<is_analytic_solution_v<initial_data>,
                           Tags::AnalyticSolution<initial_data>,
@@ -208,7 +212,7 @@ struct EvolutionMetavars {
 
   using initialization_actions = tmpl::list<
       Initialization::Actions::InitializeItems<
-          Initialization::TimeStepping<EvolutionMetavars, local_time_stepping>,
+          Initialization::TimeStepping<EvolutionMetavars, TimeStepperBase>,
           evolution::dg::Initialization::Domain<volume_dim>,
           Initialization::TimeStepperHistory<EvolutionMetavars>>,
       Initialization::Actions::AddSimpleTags<
diff --git a/src/Evolution/Executables/RelativisticEuler/Valencia/EvolveValencia.hpp b/src/Evolution/Executables/RelativisticEuler/Valencia/EvolveValencia.hpp
index 85216c9ac4e3..f18807d83251 100644
--- a/src/Evolution/Executables/RelativisticEuler/Valencia/EvolveValencia.hpp
+++ b/src/Evolution/Executables/RelativisticEuler/Valencia/EvolveValencia.hpp
@@ -122,7 +122,10 @@ struct EvolutionMetavars {
   using system = RelativisticEuler::Valencia::System<Dim>;
 
   using temporal_id = Tags::TimeStepId;
-  static constexpr bool local_time_stepping = false;
+  using TimeStepperBase = TimeStepper;
+
+  static constexpr bool local_time_stepping =
+      TimeStepperBase::local_time_stepping;
 
   using initial_data_tag =
       tmpl::conditional_t<is_analytic_solution_v<initial_data>,
@@ -227,7 +230,7 @@ struct EvolutionMetavars {
 
   using initialization_actions = tmpl::list<
       Initialization::Actions::InitializeItems<
-          Initialization::TimeStepping<EvolutionMetavars, local_time_stepping>,
+          Initialization::TimeStepping<EvolutionMetavars, TimeStepperBase>,
           evolution::dg::Initialization::Domain<Dim>,
           Initialization::TimeStepperHistory<EvolutionMetavars>>,
       Initialization::Actions::AddSimpleTags<
diff --git a/src/Evolution/Executables/ScalarAdvection/EvolveScalarAdvection.hpp b/src/Evolution/Executables/ScalarAdvection/EvolveScalarAdvection.hpp
index c46b7504fcf8..7a239b4c3096 100644
--- a/src/Evolution/Executables/ScalarAdvection/EvolveScalarAdvection.hpp
+++ b/src/Evolution/Executables/ScalarAdvection/EvolveScalarAdvection.hpp
@@ -122,7 +122,10 @@ struct EvolutionMetavars {
   static constexpr size_t volume_dim = Dim;
   using system = ScalarAdvection::System<Dim>;
   using temporal_id = Tags::TimeStepId;
-  static constexpr bool local_time_stepping = false;
+  using TimeStepperBase = TimeStepper;
+
+  static constexpr bool local_time_stepping =
+      TimeStepperBase::local_time_stepping;
 
   // The use_dg_subcell flag controls whether to use "standard" limiting (false)
   // or a DG-FD hybrid scheme (true).
@@ -302,7 +305,7 @@ struct EvolutionMetavars {
 
   using initialization_actions = tmpl::list<
       Initialization::Actions::InitializeItems<
-          Initialization::TimeStepping<EvolutionMetavars, local_time_stepping>,
+          Initialization::TimeStepping<EvolutionMetavars, TimeStepperBase>,
           evolution::dg::Initialization::Domain<volume_dim>,
           Initialization::TimeStepperHistory<EvolutionMetavars>>,
       Initialization::Actions::ConservativeSystem<system>,
diff --git a/src/Evolution/Executables/ScalarTensor/ScalarTensorBase.hpp b/src/Evolution/Executables/ScalarTensor/ScalarTensorBase.hpp
index e31ce9741d85..c83778911446 100644
--- a/src/Evolution/Executables/ScalarTensor/ScalarTensorBase.hpp
+++ b/src/Evolution/Executables/ScalarTensor/ScalarTensorBase.hpp
@@ -379,7 +379,10 @@ struct ScalarTensorTemplateBase {
 
   static constexpr size_t volume_dim = 3_st;
   using system = ScalarTensor::System;
-  static constexpr bool local_time_stepping = true;
+  using TimeStepperBase = LtsTimeStepper;
+
+  static constexpr bool local_time_stepping =
+      TimeStepperBase::local_time_stepping;
 
   // NOLINTNEXTLINE(google-runtime-references)
   void pup(PUP::er& /*p*/) {}
@@ -459,7 +462,7 @@ struct ScalarTensorTemplateBase {
   template <bool UseControlSystems>
   using initialization_actions = tmpl::list<
       Initialization::Actions::InitializeItems<
-          Initialization::TimeStepping<derived_metavars, local_time_stepping>,
+          Initialization::TimeStepping<derived_metavars, TimeStepperBase>,
           evolution::dg::Initialization::Domain<volume_dim, UseControlSystems>,
           Initialization::TimeStepperHistory<derived_metavars>>,
       Initialization::Actions::NonconservativeSystem<system>,
diff --git a/src/Evolution/Executables/ScalarWave/EvolveScalarWave.hpp b/src/Evolution/Executables/ScalarWave/EvolveScalarWave.hpp
index ce092d008a2b..1d98d98ba792 100644
--- a/src/Evolution/Executables/ScalarWave/EvolveScalarWave.hpp
+++ b/src/Evolution/Executables/ScalarWave/EvolveScalarWave.hpp
@@ -129,7 +129,10 @@ struct EvolutionMetavars {
   static constexpr dg::Formulation dg_formulation =
       dg::Formulation::StrongInertial;
   using temporal_id = Tags::TimeStepId;
-  static constexpr bool local_time_stepping = false;
+  using TimeStepperBase = TimeStepper;
+
+  static constexpr bool local_time_stepping =
+      TimeStepperBase::local_time_stepping;
 
   using analytic_solution_fields = typename system::variables_tag::tags_list;
   using deriv_compute = ::Tags::DerivCompute<
@@ -274,7 +277,7 @@ struct EvolutionMetavars {
 
   using initialization_actions = tmpl::list<
       Initialization::Actions::InitializeItems<
-          Initialization::TimeStepping<EvolutionMetavars, local_time_stepping>,
+          Initialization::TimeStepping<EvolutionMetavars, TimeStepperBase>,
           evolution::dg::Initialization::Domain<volume_dim>,
           ::amr::Initialization::Initialize<volume_dim>,
           Initialization::TimeStepperHistory<EvolutionMetavars>>,
diff --git a/src/Evolution/Initialization/Evolution.hpp b/src/Evolution/Initialization/Evolution.hpp
index 4711106c56f1..de6bfcdea451 100644
--- a/src/Evolution/Initialization/Evolution.hpp
+++ b/src/Evolution/Initialization/Evolution.hpp
@@ -80,36 +80,36 @@ void set_next_time_step_id(const gsl::not_null<TimeStepId*> next_time_step_id,
 /// Since the evolution has not started yet, initialize the state
 /// _before_ the initial time. So `Tags::TimeStepId` is undefined at this point,
 /// and `Tags::Next<Tags::TimeStepId>` is the initial time.
-template <typename Metavariables, bool UsingLts>
+template <typename Metavariables, typename TimeStepperBase>
 struct TimeStepping {
-  using TimeStepperType =
-      tmpl::conditional_t<UsingLts, LtsTimeStepper, TimeStepper>;
-
   /// Tags for constant items added to the GlobalCache.  These items are
   /// initialized from input file options.
   using const_global_cache_tags = tmpl::conditional_t<
-      UsingLts,
-      tmpl::list<::Tags::TimeStepper<TimeStepperType>, ::Tags::StepChoosers>,
-      tmpl::list<::Tags::TimeStepper<TimeStepperType>>>;
+      TimeStepperBase::local_time_stepping,
+      tmpl::list<::Tags::ConcreteTimeStepper<TimeStepperBase>,
+                 ::Tags::StepChoosers>,
+      tmpl::list<::Tags::ConcreteTimeStepper<TimeStepperBase>>>;
 
   /// Tags for mutable items added to the GlobalCache.  These items are
   /// initialized from input file options.
   using mutable_global_cache_tags = tmpl::list<>;
 
   /// Tags for items fetched by the DataBox and passed to the apply function
-  using argument_tags = tmpl::list<::Tags::Time, Tags::InitialTimeDelta,
-                                   Tags::InitialSlabSize<UsingLts>,
-                                   ::Tags::TimeStepper<TimeStepperType>>;
+  using argument_tags =
+      tmpl::list<::Tags::Time, Tags::InitialTimeDelta,
+                 Tags::InitialSlabSize<TimeStepperBase::local_time_stepping>,
+                 ::Tags::ConcreteTimeStepper<TimeStepperBase>>;
 
   /// Tags for simple DataBox items that are initialized from input file options
   using simple_tags_from_options =
       tmpl::list<::Tags::Time, Tags::InitialTimeDelta,
-                 Tags::InitialSlabSize<UsingLts>>;
+                 Tags::InitialSlabSize<TimeStepperBase::local_time_stepping>>;
 
   /// Tags for simple DataBox items that are default initialized.
-  using default_initialized_simple_tags = tmpl::push_back<
-      StepChoosers::step_chooser_simple_tags<Metavariables, UsingLts>,
-      ::Tags::TimeStepId, ::Tags::AdaptiveSteppingDiagnostics>;
+  using default_initialized_simple_tags =
+      tmpl::push_back<StepChoosers::step_chooser_simple_tags<
+                          Metavariables, TimeStepperBase::local_time_stepping>,
+                      ::Tags::TimeStepId, ::Tags::AdaptiveSteppingDiagnostics>;
 
   /// Tags for items in the DataBox that are mutated by the apply function
   using return_tags =
@@ -123,10 +123,10 @@ struct TimeStepping {
 
   /// Tags for immutable DataBox items (compute items or reference items) added
   /// to the DataBox.
-  using compute_tags = tmpl::list<>;
+  using compute_tags = time_stepper_ref_tags<TimeStepperBase>;
 
-  /// Given the items fetched from a DataBox by the argument_tags when UsingLts
-  /// is true, mutate the items in the DataBox corresponding to return_tags
+  /// Given the items fetched from a DataBox by the argument_tags when using
+  /// LTS, mutate the items in the DataBox corresponding to return_tags
   static void apply(const gsl::not_null<TimeStepId*> next_time_step_id,
                     const gsl::not_null<TimeDelta*> time_step,
                     const gsl::not_null<TimeDelta*> next_time_step,
@@ -143,8 +143,8 @@ struct TimeStepping {
     *next_time_step = *time_step;
   }
 
-  /// Given the items fetched from a DataBox by the argument_tags, when UsingLts
-  /// is false, mutate the items in the DataBox corresponding to return_tags
+  /// Given the items fetched from a DataBox by the argument_tags, when not
+  /// using LTS, mutate the items in the DataBox corresponding to return_tags
   static void apply(const gsl::not_null<TimeStepId*> next_time_step_id,
                     const gsl::not_null<TimeDelta*> time_step,
                     const gsl::not_null<TimeDelta*> next_time_step,
@@ -288,7 +288,7 @@ struct TimeStepperHistory {
   using compute_tags = tmpl::list<>;
 
   using argument_tags =
-      tmpl::list<::Tags::TimeStepper<>, domain::Tags::Mesh<dim>>;
+      tmpl::list<::Tags::TimeStepper<TimeStepper>, domain::Tags::Mesh<dim>>;
   using return_tags = simple_tags;
 
   static void apply(
diff --git a/src/Evolution/Systems/Cce/Actions/InitializeCharacteristicEvolutionTime.hpp b/src/Evolution/Systems/Cce/Actions/InitializeCharacteristicEvolutionTime.hpp
index dcdba3214638..fd3d3a10d15b 100644
--- a/src/Evolution/Systems/Cce/Actions/InitializeCharacteristicEvolutionTime.hpp
+++ b/src/Evolution/Systems/Cce/Actions/InitializeCharacteristicEvolutionTime.hpp
@@ -26,6 +26,7 @@
 #include "Time/Time.hpp"
 #include "Time/TimeStepId.hpp"
 #include "Time/TimeSteppers/LtsTimeStepper.hpp"
+#include "Time/TimeSteppers/TimeStepper.hpp"
 #include "Utilities/Rational.hpp"
 #include "Utilities/Requires.hpp"
 #include "Utilities/TMPL.hpp"
@@ -68,11 +69,11 @@ namespace Actions {
 template <typename EvolvedCoordinatesVariablesTag, typename EvolvedSwshTag,
           bool local_time_stepping>
 struct InitializeCharacteristicEvolutionTime {
-  using simple_tags_from_options = tmpl::flatten<
-      tmpl::list<Initialization::Tags::InitialSlabSize<local_time_stepping>,
-                 Tags::CceEvolutionPrefix<::Tags::TimeStepper<LtsTimeStepper>>,
-                 Tags::CceEvolutionPrefix<::Tags::StepChoosers>,
-                 ::Initialization::Tags::InitialTimeDelta>>;
+  using simple_tags_from_options = tmpl::flatten<tmpl::list<
+      Initialization::Tags::InitialSlabSize<local_time_stepping>,
+      Tags::CceEvolutionPrefix<::Tags::ConcreteTimeStepper<LtsTimeStepper>>,
+      Tags::CceEvolutionPrefix<::Tags::StepChoosers>,
+      ::Initialization::Tags::InitialTimeDelta>>;
 
   using const_global_cache_tags = tmpl::list<>;
 
@@ -83,7 +84,7 @@ struct InitializeCharacteristicEvolutionTime {
       ::Tags::AdaptiveSteppingDiagnostics,
       ::Tags::HistoryEvolvedVariables<EvolvedCoordinatesVariablesTag>,
       ::Tags::HistoryEvolvedVariables<evolved_swsh_variables_tag>>;
-  using compute_tags = tmpl::list<>;
+  using compute_tags = time_stepper_ref_tags<LtsTimeStepper>;
 
   template <typename DbTags, typename... InboxTags, typename Metavariables,
             typename ArrayIndex, typename ActionList,
@@ -113,7 +114,7 @@ struct InitializeCharacteristicEvolutionTime {
       initial_time_step = initial_time.slab().duration();
     }
 
-    const auto& time_stepper = db::get<::Tags::TimeStepper<>>(box);
+    const auto& time_stepper = db::get<::Tags::TimeStepper<TimeStepper>>(box);
 
     const size_t starting_order =
         time_stepper.number_of_past_steps() == 0 ? time_stepper.order() : 1;
diff --git a/src/Evolution/Systems/Cce/Actions/InitializeWorldtubeBoundary.hpp b/src/Evolution/Systems/Cce/Actions/InitializeWorldtubeBoundary.hpp
index 0ad5198b3912..d1b2d7f47873 100644
--- a/src/Evolution/Systems/Cce/Actions/InitializeWorldtubeBoundary.hpp
+++ b/src/Evolution/Systems/Cce/Actions/InitializeWorldtubeBoundary.hpp
@@ -67,7 +67,8 @@ struct InitializeWorldtubeBoundaryBase {
       if (dynamic_cast<const Solutions::RobinsonTrautman*>(
               &(db::get<Tags::AnalyticBoundaryDataManager>(box)
                     .get_generator())) != nullptr) {
-        if(db::get<::Tags::TimeStepper<>>(box).number_of_substeps() != 1) {
+        if (db::get<::Tags::TimeStepper<TimeStepper>>(box)
+                .number_of_substeps() != 1) {
           ERROR(
               "Do not use RobinsonTrautman analytic solution with a "
               "substep-based timestepper. This is to prevent severe slowdowns "
@@ -189,19 +190,22 @@ struct InitializeWorldtubeBoundary<AnalyticWorldtubeBoundary<Metavariables>>
     : public detail::InitializeWorldtubeBoundaryBase<
           InitializeWorldtubeBoundary<AnalyticWorldtubeBoundary<Metavariables>>,
           tmpl::list<Tags::AnalyticBoundaryDataManager,
-                     Tags::CceEvolutionPrefix<::Tags::TimeStepper<
+                     Tags::CceEvolutionPrefix<::Tags::ConcreteTimeStepper<
                          tmpl::conditional_t<Metavariables::local_time_stepping,
                                              LtsTimeStepper, TimeStepper>>>>,
           typename Metavariables::cce_boundary_communication_tags> {
+  using TimeStepperType =
+      tmpl::conditional_t<Metavariables::local_time_stepping, LtsTimeStepper,
+                          TimeStepper>;
   using base_type = detail::InitializeWorldtubeBoundaryBase<
       InitializeWorldtubeBoundary<AnalyticWorldtubeBoundary<Metavariables>>,
       tmpl::list<Tags::AnalyticBoundaryDataManager,
-                 Tags::CceEvolutionPrefix<::Tags::TimeStepper<
-                     tmpl::conditional_t<Metavariables::local_time_stepping,
-                                         LtsTimeStepper, TimeStepper>>>>,
+                 Tags::CceEvolutionPrefix<
+                     ::Tags::ConcreteTimeStepper<TimeStepperType>>>,
       typename Metavariables::cce_boundary_communication_tags>;
   using base_type::apply;
   using typename base_type::simple_tags;
+  using compute_tags = time_stepper_ref_tags<TimeStepperType>;
   using const_global_cache_tags =
       tmpl::list<Tags::LMax, Tags::SpecifiedEndTime, Tags::SpecifiedStartTime>;
   using typename base_type::simple_tags_from_options;
diff --git a/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/ChangeSlabSize.hpp b/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/ChangeSlabSize.hpp
index 0e546c69087d..1bdce76a0412 100644
--- a/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/ChangeSlabSize.hpp
+++ b/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/ChangeSlabSize.hpp
@@ -14,9 +14,7 @@
 #include "Parallel/GlobalCache.hpp"
 #include "ParallelAlgorithms/EventsAndTriggers/Tags.hpp"
 #include "Time/Actions/ChangeSlabSize.hpp"
-#include "Time/Tags/TimeStepper.hpp"
 #include "Time/TimeStepId.hpp"
-#include "Time/TimeSteppers/TimeStepper.hpp"
 #include "Utilities/Gsl.hpp"
 #include "Utilities/TMPL.hpp"
 
@@ -24,7 +22,10 @@
 namespace Tags {
 struct TimeStep;
 struct TimeStepId;
+template <typename StepperInterface>
+struct TimeStepper;
 }  // namespace Tags
+class TimeStepper;
 /// \endcond
 
 namespace CurvedScalarWave::Worldtube::Actions {
@@ -73,8 +74,8 @@ struct ChangeSlabSize {
           "different.");
       const auto new_step = inbox_slab.duration();
       const auto new_next_time_step_id =
-          db::get<::Tags::TimeStepper<>>(box).next_time_id(inbox_time_step_id,
-                                                           new_step);
+          db::get<::Tags::TimeStepper<TimeStepper>>(box).next_time_id(
+              inbox_time_step_id, new_step);
       db::mutate<::Tags::Next<::Tags::TimeStepId>, ::Tags::TimeStep,
                  ::Tags::Next<::Tags::TimeStep>, ::Tags::TimeStepId>(
           [&new_next_time_step_id, &new_step, &inbox_time_step_id](
diff --git a/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/InitializeEvolvedVariables.hpp b/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/InitializeEvolvedVariables.hpp
index f9b48efb9699..5bf544c147ec 100644
--- a/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/InitializeEvolvedVariables.hpp
+++ b/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/InitializeEvolvedVariables.hpp
@@ -10,10 +10,16 @@
 #include "DataStructures/VariablesTag.hpp"
 #include "Evolution/Systems/CurvedScalarWave/Worldtube/Tags.hpp"
 #include "Time/Tags/HistoryEvolvedVariables.hpp"
-#include "Time/Tags/TimeStepper.hpp"
 #include "Time/TimeSteppers/TimeStepper.hpp"
 #include "Utilities/Gsl.hpp"
 
+/// \cond
+namespace Tags {
+template <typename StepperInterface>
+struct TimeStepper;
+}  // namespace Tags
+/// \endcond
+
 namespace CurvedScalarWave::Worldtube::Initialization {
 /*!
  * \brief Initializes the time stepper and evolved variables used by the
@@ -36,7 +42,7 @@ struct InitializeEvolvedVariables {
   using simple_tags_from_options = tmpl::list<>;
   using const_global_cache_tags = tmpl::list<>;
   using mutable_global_cache_tags = tmpl::list<>;
-  using argument_tags = tmpl::list<::Tags::TimeStepper<>>;
+  using argument_tags = tmpl::list<::Tags::TimeStepper<TimeStepper>>;
   static void apply(
       const gsl::not_null<Variables<tmpl::list<Tags::Psi0, Tags::dtPsi0>>*>
           evolved_vars,
diff --git a/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonChare.hpp b/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonChare.hpp
index 901febdd0322..e78aa2d76916 100644
--- a/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonChare.hpp
+++ b/src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonChare.hpp
@@ -59,11 +59,15 @@ struct WorldtubeSingleton {
   using metavariables = Metavariables;
   using evolved_vars = ::Tags::Variables<
       tmpl::list<CurvedScalarWave::Tags::Psi, CurvedScalarWave::Tags::Pi>>;
-  // not currently supported
-  static constexpr bool local_time_stepping = false;
+  // LTS not currently supported
+  using TimeStepperBase = TimeStepper;
+
+  static constexpr bool local_time_stepping =
+      TimeStepperBase::local_time_stepping;
+
   using initialization_actions = tmpl::list<
       ::Initialization::Actions::InitializeItems<
-          ::Initialization::TimeStepping<Metavariables, local_time_stepping>,
+          ::Initialization::TimeStepping<Metavariables, TimeStepperBase>,
           Initialization::InitializeEvolvedVariables,
           Initialization::InitializeSpacetimeTags,
           Initialization::InitializeElementFacesGridCoordinates<Dim>>,
diff --git a/src/Executables/ExportCoordinates/ExportCoordinates.hpp b/src/Executables/ExportCoordinates/ExportCoordinates.hpp
index 868c5384d82f..c1c30b45ae5d 100644
--- a/src/Executables/ExportCoordinates/ExportCoordinates.hpp
+++ b/src/Executables/ExportCoordinates/ExportCoordinates.hpp
@@ -265,7 +265,11 @@ struct SetMeshType {
 template <size_t Dim, bool EnableTimeDependentMaps>
 struct Metavariables {
   static constexpr size_t volume_dim = Dim;
-  static constexpr bool local_time_stepping = false;
+  using TimeStepperBase = TimeStepper;
+
+  static constexpr bool local_time_stepping =
+      TimeStepperBase::local_time_stepping;
+
   // A placeholder system for the domain creators
   struct system {};
 
@@ -334,7 +338,7 @@ struct Metavariables {
               Parallel::Phase::Initialization,
               tmpl::list<Initialization::Actions::InitializeItems<
                              Initialization::TimeStepping<Metavariables,
-                                                          local_time_stepping>,
+                                                          TimeStepperBase>,
                              evolution::dg::Initialization::Domain<Dim>,
                              ::amr::Initialization::Initialize<volume_dim>,
                              Initialization::SetMeshType<Dim>>,
diff --git a/src/Time/Actions/AdvanceTime.hpp b/src/Time/Actions/AdvanceTime.hpp
index 35361080a80e..cb87c9e35c8a 100644
--- a/src/Time/Actions/AdvanceTime.hpp
+++ b/src/Time/Actions/AdvanceTime.hpp
@@ -13,7 +13,6 @@
 #include "Parallel/AlgorithmExecution.hpp"
 #include "Time/AdaptiveSteppingDiagnostics.hpp"
 #include "Time/Tags/AdaptiveSteppingDiagnostics.hpp"
-#include "Time/Tags/TimeStepper.hpp"
 #include "Time/Time.hpp"
 #include "Time/TimeStepId.hpp"
 #include "Time/TimeSteppers/TimeStepper.hpp"
@@ -32,6 +31,8 @@ struct Next;
 struct Time;
 struct TimeStep;
 struct TimeStepId;
+template <typename StepperInterface>
+struct TimeStepper;
 }  // namespace Tags
 // IWYU pragma: no_forward_declare db::DataBox
 /// \endcond
@@ -48,7 +49,7 @@ namespace Actions {
 /// - DataBox:
 ///   - Tags::Next<Tags::TimeStep>
 ///   - Tags::Next<Tags::TimeStepId>
-///   - Tags::TimeStepper<>
+///   - Tags::TimeStepper<TimeStepper>
 ///
 /// DataBox changes:
 ///   - Tags::Next<Tags::TimeStepId>
@@ -110,7 +111,7 @@ struct AdvanceTime {
               time_step->with_slab(next_time_id->step_time().slab());
           *time = time_id->substep_time();
         },
-        make_not_null(&box), db::get<Tags::TimeStepper<>>(box),
+        make_not_null(&box), db::get<Tags::TimeStepper<TimeStepper>>(box),
         is_using_error_control);
 
     return {Parallel::AlgorithmExecution::Continue, std::nullopt};
diff --git a/src/Time/Actions/ChangeSlabSize.hpp b/src/Time/Actions/ChangeSlabSize.hpp
index bdc54aec3f90..76dded60b741 100644
--- a/src/Time/Actions/ChangeSlabSize.hpp
+++ b/src/Time/Actions/ChangeSlabSize.hpp
@@ -33,7 +33,6 @@
 #include "Time/ChangeSlabSize.hpp"
 #include "Time/StepChoosers/StepChooser.hpp"
 #include "Time/Tags/HistoryEvolvedVariables.hpp"
-#include "Time/Tags/TimeStepper.hpp"
 #include "Time/TimeStepId.hpp"
 #include "Time/TimeSteppers/TimeStepper.hpp"
 #include "Utilities/Algorithm.hpp"
@@ -47,6 +46,8 @@
 namespace Tags {
 struct DataBox;
 struct TimeStepId;
+template <typename StepperInterface>
+struct TimeStepper;
 }  // namespace Tags
 /// \endcond
 
@@ -127,7 +128,7 @@ namespace Actions {
 ///   - Tags::HistoryEvolvedVariables
 ///   - Tags::TimeStep
 ///   - Tags::TimeStepId
-///   - Tags::TimeStepper<>
+///   - Tags::TimeStepper<TimeStepper>
 ///
 /// DataBox changes:
 /// - Adds: nothing
@@ -195,7 +196,8 @@ struct ChangeSlabSize {
         *alg::min_element(new_slab_size_inbox.begin()->second);
     new_slab_size_inbox.erase(new_slab_size_inbox.begin());
 
-    const TimeStepper& time_stepper = db::get<::Tags::TimeStepper<>>(box);
+    const TimeStepper& time_stepper =
+        db::get<::Tags::TimeStepper<TimeStepper>>(box);
 
     // Sometimes time steppers need to run with a fixed step size.
     // This is generally at the start of an evolution when the history
diff --git a/src/Time/Actions/ChangeStepSize.hpp b/src/Time/Actions/ChangeStepSize.hpp
index 19d86c2958f9..285be96cfd28 100644
--- a/src/Time/Actions/ChangeStepSize.hpp
+++ b/src/Time/Actions/ChangeStepSize.hpp
@@ -15,7 +15,6 @@
 #include "Time/ChooseLtsStepSize.hpp"
 #include "Time/Tags/AdaptiveSteppingDiagnostics.hpp"
 #include "Time/Tags/HistoryEvolvedVariables.hpp"
-#include "Time/Tags/TimeStepper.hpp"
 #include "Time/TimeSteppers/LtsTimeStepper.hpp"
 #include "Utilities/Gsl.hpp"
 #include "Utilities/TMPL.hpp"
@@ -38,6 +37,8 @@ struct Next;
 struct StepChoosers;
 struct TimeStep;
 struct TimeStepId;
+template <typename StepperInterface>
+struct TimeStepper;
 }  // namespace Tags
 // IWYU pragma: no_forward_declare db::DataBox
 /// \endcond
@@ -53,7 +54,8 @@ struct TimeStepId;
 /// choosers that may not be compatible with all components.
 template <typename StepChoosersToUse = AllStepChoosers, typename DbTags>
 bool change_step_size(const gsl::not_null<db::DataBox<DbTags>*> box) {
-  const LtsTimeStepper& time_stepper = db::get<Tags::TimeStepper<>>(*box);
+  const LtsTimeStepper& time_stepper =
+      db::get<Tags::TimeStepper<LtsTimeStepper>>(*box);
   const auto& step_choosers = db::get<Tags::StepChoosers>(*box);
 
   const auto& next_time_id = db::get<Tags::Next<Tags::TimeStepId>>(*box);
@@ -144,7 +146,7 @@ namespace Actions {
 ///   - Tags::HistoryEvolvedVariables
 ///   - Tags::TimeStep
 ///   - Tags::TimeStepId
-///   - Tags::TimeStepper<>
+///   - Tags::TimeStepper<LtsTimeStepper>
 ///
 /// DataBox changes:
 /// - Adds: nothing
diff --git a/src/Time/Actions/SelfStartActions.hpp b/src/Time/Actions/SelfStartActions.hpp
index 2b7bd4c18bc6..ddd883d25204 100644
--- a/src/Time/Actions/SelfStartActions.hpp
+++ b/src/Time/Actions/SelfStartActions.hpp
@@ -21,7 +21,6 @@
 #include "Time/Slab.hpp"
 #include "Time/Tags/HistoryEvolvedVariables.hpp"
 #include "Time/Tags/TimeStep.hpp"
-#include "Time/Tags/TimeStepper.hpp"
 #include "Time/Time.hpp"
 #include "Time/TimeStepId.hpp"
 #include "Utilities/Gsl.hpp"
@@ -38,7 +37,10 @@ class GlobalCache;
 }  // namespace Parallel
 namespace Tags {
 struct TimeStepId;
+template <typename StepperInterface>
+struct TimeStepper;
 }  // namespace Tags
+class TimeStepper;
 /// \endcond
 
 /// \ingroup TimeGroup
@@ -219,7 +221,7 @@ struct Initialize {
     const auto values_needed =
         db::get<::Tags::Next<::Tags::TimeStepId>>(box).slab_number() == 0
             ? 0
-            : db::get<::Tags::TimeStepper<>>(box).order() - 1;
+            : db::get<::Tags::TimeStepper<TimeStepper>>(box).order() - 1;
 
     TimeDelta self_start_step = initial_step;
 
@@ -453,11 +455,11 @@ struct Cleanup {
     tmpl::for_each<history_tags>([&box](auto tag_v) {
       using tag = typename decltype(tag_v)::type;
       ASSERT(db::get<tag>(box).integration_order() ==
-                 db::get<::Tags::TimeStepper<>>(box).order(),
+                 db::get<::Tags::TimeStepper<TimeStepper>>(box).order(),
              "Volume history order is: "
                  << db::get<tag>(box).integration_order()
                  << " but time stepper requires order: "
-                 << db::get<::Tags::TimeStepper<>>(box).order()
+                 << db::get<::Tags::TimeStepper<TimeStepper>>(box).order()
                  << ". This may indicate that the step size has varied during "
                     "self-start, which should not be permitted.");
     });
diff --git a/src/Time/Actions/UpdateU.hpp b/src/Time/Actions/UpdateU.hpp
index 751621ce40ae..956e4b483c55 100644
--- a/src/Time/Actions/UpdateU.hpp
+++ b/src/Time/Actions/UpdateU.hpp
@@ -16,7 +16,7 @@
 #include "Time/Tags/HistoryEvolvedVariables.hpp"
 #include "Time/Tags/PreviousStepperError.hpp"
 #include "Time/Tags/StepperError.hpp"
-#include "Time/Tags/TimeStepper.hpp"
+#include "Time/TimeSteppers/TimeStepper.hpp"
 #include "Utilities/Gsl.hpp"
 #include "Utilities/SetNumberOfGridPoints.hpp"
 #include "Utilities/TMPL.hpp"
@@ -34,6 +34,8 @@ namespace Tags {
 struct IsUsingTimeSteppingErrorControl;
 struct StepperErrorUpdated;
 struct TimeStep;
+template <typename StepperInterface>
+struct TimeStepper;
 }  // namespace Tags
 /// \endcond
 
@@ -59,7 +61,7 @@ void update_one_variables(const gsl::not_null<db::DataBox<DbTags>*> box) {
              const gsl::not_null<typename previous_error_tag::type*>
                  previous_error,
              const gsl::not_null<typename history_tag::type*> history,
-             const ::TimeDelta& time_step, const auto& time_stepper) {
+             const ::TimeDelta& time_step, const TimeStepper& time_stepper) {
             using std::swap;
             set_number_of_grid_points(previous_error, *vars);
             swap(*error, *previous_error);
@@ -70,7 +72,7 @@ void update_one_variables(const gsl::not_null<db::DataBox<DbTags>*> box) {
             }
           },
           box, db::get<Tags::TimeStep>(*box),
-          db::get<Tags::TimeStepper<>>(*box));
+          db::get<Tags::TimeStepper<TimeStepper>>(*box));
     } else {
       ERROR(
           "Cannot update the stepper error measure -- "
@@ -80,10 +82,11 @@ void update_one_variables(const gsl::not_null<db::DataBox<DbTags>*> box) {
     db::mutate<VariablesTag, history_tag>(
         [](const gsl::not_null<typename VariablesTag::type*> vars,
            const gsl::not_null<typename history_tag::type*> history,
-           const ::TimeDelta& time_step, const auto& time_stepper) {
+           const ::TimeDelta& time_step, const TimeStepper& time_stepper) {
           time_stepper.update_u(vars, history, time_step);
         },
-        box, db::get<Tags::TimeStep>(*box), db::get<Tags::TimeStepper<>>(*box));
+        box, db::get<Tags::TimeStep>(*box),
+        db::get<Tags::TimeStepper<TimeStepper>>(*box));
   }
 }
 }  // namespace update_u_detail
@@ -121,7 +124,7 @@ namespace Actions {
 ///   - system::variables_tag
 ///   - Tags::HistoryEvolvedVariables<variables_tag>
 ///   - Tags::TimeStep
-///   - Tags::TimeStepper<>
+///   - Tags::TimeStepper<TimeStepper>
 ///   - Tags::IsUsingTimeSteppingErrorControl
 ///
 /// DataBox changes:
diff --git a/src/Time/ChangeSlabSize.hpp b/src/Time/ChangeSlabSize.hpp
index a17b93eac55f..f80f07c6d6c4 100644
--- a/src/Time/ChangeSlabSize.hpp
+++ b/src/Time/ChangeSlabSize.hpp
@@ -7,7 +7,6 @@
 #include "Time/AdaptiveSteppingDiagnostics.hpp"
 #include "Time/Slab.hpp"
 #include "Time/Tags/HistoryEvolvedVariables.hpp"
-#include "Time/Tags/TimeStepper.hpp"
 #include "Time/Time.hpp"
 #include "Time/TimeStepId.hpp"
 #include "Utilities/ErrorHandling/Assert.hpp"
@@ -21,7 +20,10 @@ template <typename Tag>
 struct Next;
 struct TimeStep;
 struct TimeStepId;
+template <typename StepperInterface>
+struct TimeStepper;
 }  // namespace Tags
+class TimeStepper;
 /// \endcond
 
 /// \ingroup TimeGroup
@@ -61,8 +63,8 @@ void change_slab_size(const gsl::not_null<db::DataBox<DbTags>*> box,
   const auto new_time_step = old_time_step.with_slab(new_slab);
 
   const auto new_next_time_step_id =
-      db::get<Tags::TimeStepper<>>(*box).next_time_id(new_time_step_id,
-                                                      new_time_step);
+      db::get<Tags::TimeStepper<TimeStepper>>(*box).next_time_id(
+          new_time_step_id, new_time_step);
 
   db::mutate_apply<
       tmpl::push_front<Tags::get_all_history_tags<DbTags>,
diff --git a/src/Time/StepChoosers/Cfl.hpp b/src/Time/StepChoosers/Cfl.hpp
index 4ae7ee511b6c..6c77b1e46114 100644
--- a/src/Time/StepChoosers/Cfl.hpp
+++ b/src/Time/StepChoosers/Cfl.hpp
@@ -12,12 +12,15 @@
 #include "Domain/MinimumGridSpacing.hpp"
 #include "Options/String.hpp"
 #include "Time/StepChoosers/StepChooser.hpp"  // IWYU pragma: keep
-#include "Time/Tags/TimeStepper.hpp"
 #include "Time/TimeSteppers/TimeStepper.hpp"
 #include "Utilities/Serialization/CharmPupable.hpp"
 #include "Utilities/TMPL.hpp"
 
 /// \cond
+namespace Tags {
+template <typename StepperInterface>
+struct TimeStepper;
+}  // namespace Tags
 namespace domain {
 namespace Tags {
 template <size_t Dim, typename Frame>
@@ -53,7 +56,7 @@ class Cfl : public StepChooser<StepChooserUse> {
 
   using argument_tags =
       tmpl::list<domain::Tags::MinimumGridSpacing<System::volume_dim, Frame>,
-                 ::Tags::TimeStepper<>,
+                 ::Tags::TimeStepper<TimeStepper>,
                  typename System::compute_largest_characteristic_speed>;
 
   using compute_tags = tmpl::list<
diff --git a/src/Time/StepChoosers/ElementSizeCfl.hpp b/src/Time/StepChoosers/ElementSizeCfl.hpp
index f61947ab46ef..ef78d3263500 100644
--- a/src/Time/StepChoosers/ElementSizeCfl.hpp
+++ b/src/Time/StepChoosers/ElementSizeCfl.hpp
@@ -12,12 +12,15 @@
 #include "Domain/SizeOfElement.hpp"
 #include "Options/String.hpp"
 #include "Time/StepChoosers/StepChooser.hpp"
-#include "Time/Tags/TimeStepper.hpp"
 #include "Time/TimeSteppers/TimeStepper.hpp"
 #include "Utilities/Serialization/CharmPupable.hpp"
 #include "Utilities/TMPL.hpp"
 
 /// \cond
+namespace Tags {
+template <typename StepperInterface>
+struct TimeStepper;
+}  // namespace Tags
 namespace domain {
 namespace Tags {
 template <size_t Dim>
@@ -60,7 +63,8 @@ class ElementSizeCfl : public StepChooser<StepChooserUse> {
       : safety_factor_(safety_factor) {}
 
   using argument_tags =
-      tmpl::list<::Tags::TimeStepper<>, domain::Tags::SizeOfElement<Dim>,
+      tmpl::list<::Tags::TimeStepper<TimeStepper>,
+                 domain::Tags::SizeOfElement<Dim>,
                  typename System::compute_largest_characteristic_speed>;
   using compute_tags =
       tmpl::list<domain::Tags::SizeOfElementCompute<Dim>,
diff --git a/src/Time/StepChoosers/ErrorControl.hpp b/src/Time/StepChoosers/ErrorControl.hpp
index 5742d43cbe89..4eee3f6184d0 100644
--- a/src/Time/StepChoosers/ErrorControl.hpp
+++ b/src/Time/StepChoosers/ErrorControl.hpp
@@ -26,7 +26,6 @@
 #include "Time/Tags/PreviousStepperError.hpp"
 #include "Time/Tags/StepperError.hpp"
 #include "Time/Tags/StepperErrorUpdated.hpp"
-#include "Time/Tags/TimeStepper.hpp"
 #include "Time/TimeSteppers/TimeStepper.hpp"
 #include "Utilities/Serialization/CharmPupable.hpp"
 #include "Utilities/Serialization/PupStlCpp17.hpp"
@@ -38,6 +37,8 @@ namespace Tags {
 template <bool LocalTimeStepping>
 struct IsUsingTimeSteppingErrorControlCompute;
 struct StepChoosers;
+template <typename StepperInterface>
+struct TimeStepper;
 }  // namespace Tags
 /// \endcond
 
@@ -193,7 +194,7 @@ class ErrorControl : public StepChooser<StepChooserUse>,
       tmpl::list<::Tags::HistoryEvolvedVariables<EvolvedVariableTag>,
                  ::Tags::StepperError<EvolvedVariableTag>,
                  ::Tags::PreviousStepperError<EvolvedVariableTag>,
-                 ::Tags::StepperErrorUpdated, ::Tags::TimeStepper<>>;
+                 ::Tags::StepperErrorUpdated, ::Tags::TimeStepper<TimeStepper>>;
 
   std::pair<double, bool> operator()(
       const TimeSteppers::History<evolved_variable_type>& history,
diff --git a/src/Time/Tags/TimeStepper.hpp b/src/Time/Tags/TimeStepper.hpp
index 19f103a158f1..b68618a0649e 100644
--- a/src/Time/Tags/TimeStepper.hpp
+++ b/src/Time/Tags/TimeStepper.hpp
@@ -13,18 +13,15 @@
 namespace Tags {
 /// \ingroup DataBoxTagsGroup
 /// \ingroup TimeGroup
-/// \brief Tag for a ::TimeStepper of type `StepperType`.
+/// The evolution TimeStepper.  The template parameter should be one
+/// of the time stepper base classes, such as `TimeStepper` or
+/// `LtsTimeStepper`.
 ///
-/// Leaving the template parameter unspecified gives a base tag.
-template <typename StepperType = void>
-struct TimeStepper;
-
-/// \cond
-template <>
-struct TimeStepper<> : db::BaseTag {};
-
+/// For the contained object to be used, the reference tags listed in
+/// `time_stepper_ref_tags<StepperType>` will also need to be added to
+/// the DataBox.
 template <typename StepperType>
-struct TimeStepper : TimeStepper<>, db::SimpleTag {
+struct ConcreteTimeStepper : db::SimpleTag {
   using type = std::unique_ptr<StepperType>;
   using option_tags = tmpl::list<::OptionTags::TimeStepper<StepperType>>;
 
@@ -34,5 +31,42 @@ struct TimeStepper : TimeStepper<>, db::SimpleTag {
     return deserialize<type>(serialize<type>(time_stepper).data());
   }
 };
-/// \endcond
+
+/// \ingroup DataBoxTagsGroup
+/// \ingroup TimeGroup
+/// Access to a time stepper through the `StepperInterface` interface
+/// (such as `TimeStepper` or `LtsTimeStepper`).
+///
+/// \details This tag cannot be added directly to the DataBox of
+/// GlobalCache because it contains an abstract type, but can only be
+/// used for retrieving the time stepper.  Instead, the
+/// `ConcreteTimeStepper` tag should be added, along with the
+/// reference tags given by `time_stepper_ref_tags`.
+template <typename StepperInterface>
+struct TimeStepper : db::SimpleTag {
+  using type = StepperInterface;
+};
+
+/// \ingroup DataBoxTagsGroup
+/// \ingroup TimeGroup
+/// Reference tag to provide access to the time stepper through its
+/// provided interfaces, such as `Tags::TimeStepper<TimeStepper>` and
+/// `Tags::TimeStepper<LtsTimeStepper>`.  Usually added through the
+/// `time_stepper_ref_tags` alias.
+template <typename StepperInterface, typename StepperType>
+struct TimeStepperRef : TimeStepper<StepperInterface>, db::ReferenceTag {
+  using base = TimeStepper<StepperInterface>;
+  using argument_tags = tmpl::list<ConcreteTimeStepper<StepperType>>;
+  static const StepperInterface& get(const StepperType& stepper) {
+    return stepper;
+  }
+};
 }  // namespace Tags
+
+/// \ingroup TimeGroup
+/// List of Tags::TimeStepperRef specializations needed when adding a
+/// Tags::ConcreteTimeStepper.
+template <typename StepperType>
+using time_stepper_ref_tags = tmpl::transform<
+    typename StepperType::provided_time_stepper_interfaces,
+    tmpl::bind<::Tags::TimeStepperRef, tmpl::_1, tmpl::pin<StepperType>>>;
diff --git a/src/Time/TimeSteppers/ImexTimeStepper.hpp b/src/Time/TimeSteppers/ImexTimeStepper.hpp
index 615c3b52039a..e548651867a0 100644
--- a/src/Time/TimeSteppers/ImexTimeStepper.hpp
+++ b/src/Time/TimeSteppers/ImexTimeStepper.hpp
@@ -62,6 +62,10 @@
  */
 class ImexTimeStepper : public virtual TimeStepper {
  public:
+  static constexpr bool imex = true;
+  using provided_time_stepper_interfaces =
+      tmpl::list<ImexTimeStepper, TimeStepper>;
+
   WRAPPED_PUPable_abstract(ImexTimeStepper);  // NOLINT
 
 /// \cond
diff --git a/src/Time/TimeSteppers/LtsTimeStepper.hpp b/src/Time/TimeSteppers/LtsTimeStepper.hpp
index 3e2e4244ce0c..8f3ad93dcb67 100644
--- a/src/Time/TimeSteppers/LtsTimeStepper.hpp
+++ b/src/Time/TimeSteppers/LtsTimeStepper.hpp
@@ -39,6 +39,10 @@ class TimeStepId;
 /// placed in the cpp file.
 class LtsTimeStepper : public virtual TimeStepper {
  public:
+  static constexpr bool local_time_stepping = true;
+  using provided_time_stepper_interfaces =
+      tmpl::list<LtsTimeStepper, TimeStepper>;
+
   WRAPPED_PUPable_abstract(LtsTimeStepper);  // NOLINT
 
   // These two are defined as separate type aliases to keep the
diff --git a/src/Time/TimeSteppers/TimeStepper.hpp b/src/Time/TimeSteppers/TimeStepper.hpp
index 1330a14e0d24..35a67151034e 100644
--- a/src/Time/TimeSteppers/TimeStepper.hpp
+++ b/src/Time/TimeSteppers/TimeStepper.hpp
@@ -42,6 +42,10 @@ namespace TimeSteppers {}
 /// in the cpp file.
 class TimeStepper : public PUP::able {
  public:
+  static constexpr bool local_time_stepping = false;
+  static constexpr bool imex = false;
+  using provided_time_stepper_interfaces = tmpl::list<TimeStepper>;
+
   WRAPPED_PUPable_abstract(TimeStepper);  // NOLINT
 
   /// \cond
diff --git a/tests/Unit/ControlSystem/Actions/Test_LimitTimeStep.cpp b/tests/Unit/ControlSystem/Actions/Test_LimitTimeStep.cpp
index 663f52b1ddb6..cf014ae1d27e 100644
--- a/tests/Unit/ControlSystem/Actions/Test_LimitTimeStep.cpp
+++ b/tests/Unit/ControlSystem/Actions/Test_LimitTimeStep.cpp
@@ -82,10 +82,10 @@ struct Component {
   using simple_tags = db::AddSimpleTags<
       control_system::Tags::FutureMeasurements<systemsA>,
       control_system::Tags::FutureMeasurements<systemsB>,
-      Tags::TimeStepper<TimeStepper>, Tags::TimeStepId,
+      Tags::ConcreteTimeStepper<TimeStepper>, Tags::TimeStepId,
       Tags::Next<Tags::TimeStepId>, Tags::TimeStep, Tags::Next<Tags::TimeStep>,
       Tags::AdaptiveSteppingDiagnostics, Tags::HistoryEvolvedVariables<Var>>;
-  using compute_tags = db::AddComputeTags<>;
+  using compute_tags = time_stepper_ref_tags<TimeStepper>;
   using phase_dependent_action_list = tmpl::list<
       Parallel::PhaseActions<Parallel::Phase::Initialization,
                              tmpl::list<ActionTesting::InitializeDataBox<
diff --git a/tests/Unit/Evolution/Actions/Test_RunEventsAndDenseTriggers.cpp b/tests/Unit/Evolution/Actions/Test_RunEventsAndDenseTriggers.cpp
index 54d77d31cd1e..e9cd4b356c6b 100644
--- a/tests/Unit/Evolution/Actions/Test_RunEventsAndDenseTriggers.cpp
+++ b/tests/Unit/Evolution/Actions/Test_RunEventsAndDenseTriggers.cpp
@@ -274,11 +274,16 @@ struct Component {
                        Tags::HistoryEvolvedVariables<variables_tag>,
                        evolution::Tags::EventsAndDenseTriggers,
                        domain::Tags::NeighborMesh<1>, domain::Tags::Element<1>>;
-
-  using phase_dependent_action_list = tmpl::list<Parallel::PhaseActions<
-      Parallel::Phase::Testing,
-      tmpl::list<evolution::Actions::RunEventsAndDenseTriggers<
-          typename Metavariables::postprocessors>>>>;
+  using compute_tags = time_stepper_ref_tags<TimeStepper>;
+
+  using phase_dependent_action_list = tmpl::list<
+      Parallel::PhaseActions<Parallel::Phase::Initialization,
+                             tmpl::list<ActionTesting::InitializeDataBox<
+                                 tmpl::list<>, compute_tags>>>,
+      Parallel::PhaseActions<
+          Parallel::Phase::Testing,
+          tmpl::list<evolution::Actions::RunEventsAndDenseTriggers<
+              typename Metavariables::postprocessors>>>>;
 };
 
 template <typename Postprocessors>
@@ -286,7 +291,8 @@ struct Metavariables {
   using postprocessors = Postprocessors;
   using system = System;
   using component_list = tmpl::list<Component<Metavariables>>;
-  using const_global_cache_tags = tmpl::list<Tags::TimeStepper<TimeStepper>>;
+  using const_global_cache_tags =
+      tmpl::list<Tags::ConcreteTimeStepper<TimeStepper>>;
   struct factory_creation
       : tt::ConformsTo<Options::protocols::FactoryCreation> {
     using factory_classes =
@@ -368,9 +374,9 @@ void test(const bool time_runs_forward) {
         }
 
         tmpl::as_pack<extra_data>([&](auto... tags_v) {
-          ActionTesting::emplace_array_component<component>(
+          ActionTesting::emplace_array_component_and_initialize<component>(
               runner, ActionTesting::NodeId{0}, ActionTesting::LocalCoreId{0},
-              0, time_step_id, exact_step_size, start_time,
+              0, {}, time_step_id, exact_step_size, start_time,
               std::optional<double>{}, stored_vars, std::move(history),
               evolution::EventsAndDenseTriggers(
                   std::move(events_and_dense_triggers)),
@@ -510,7 +516,7 @@ void test(const bool time_runs_forward) {
                         time_step_id.step_time().slab().duration() / 4),
                 initial_vars, deriv_vars);
           },
-          make_not_null(&box), db::get<Tags::TimeStepper<>>(box));
+          make_not_null(&box), db::get<Tags::TimeStepper<TimeStepper>>(box));
     }
     if (data_needed) {
       TestCase::check_dense(&runner, true, {});
diff --git a/tests/Unit/Evolution/DgSubcell/Actions/Test_TciAndSwitchToDg.cpp b/tests/Unit/Evolution/DgSubcell/Actions/Test_TciAndSwitchToDg.cpp
index 71b3101f1865..6f37d2f27848 100644
--- a/tests/Unit/Evolution/DgSubcell/Actions/Test_TciAndSwitchToDg.cpp
+++ b/tests/Unit/Evolution/DgSubcell/Actions/Test_TciAndSwitchToDg.cpp
@@ -90,15 +90,16 @@ struct component {
       evolution::dg::subcell::Tags::TciGridHistory,
       Tags::Variables<tmpl::list<Var1>>,
       Tags::HistoryEvolvedVariables<Tags::Variables<tmpl::list<Var1>>>,
-      Tags::TimeStepper<TimeStepper>,
+      Tags::ConcreteTimeStepper<TimeStepper>,
       evolution::dg::subcell::Tags::NeighborTciDecisions<Dim>,
       domain::Tags::Element<Dim>,
       evolution::dg::subcell::Tags::CellCenteredFlux<
           typename metavariables::system::flux_variables, Dim>>;
+  using compute_tags = time_stepper_ref_tags<TimeStepper>;
 
   using phase_dependent_action_list = tmpl::list<Parallel::PhaseActions<
       Parallel::Phase::Initialization,
-      tmpl::list<ActionTesting::InitializeDataBox<initial_tags>,
+      tmpl::list<ActionTesting::InitializeDataBox<initial_tags, compute_tags>,
                  evolution::dg::subcell::Actions::TciAndSwitchToDg<
                      typename Metavariables::TciOnSubcellGrid>>>>;
 };
diff --git a/tests/Unit/Evolution/DiscontinuousGalerkin/Actions/Test_ApplyBoundaryCorrections.cpp b/tests/Unit/Evolution/DiscontinuousGalerkin/Actions/Test_ApplyBoundaryCorrections.cpp
index 0cbf7395efd1..3c97221494ba 100644
--- a/tests/Unit/Evolution/DiscontinuousGalerkin/Actions/Test_ApplyBoundaryCorrections.cpp
+++ b/tests/Unit/Evolution/DiscontinuousGalerkin/Actions/Test_ApplyBoundaryCorrections.cpp
@@ -398,7 +398,7 @@ struct component {
 
   using simple_tags = tmpl::list<
       ::Tags::TimeStepId, ::Tags::Next<::Tags::TimeStepId>, ::Tags::TimeStep,
-      Tags::TimeStepper<TimeSteppers::AdamsBashforth>,
+      Tags::ConcreteTimeStepper<LtsTimeStepper>,
       db::add_tag_prefix<::Tags::dt,
                          typename Metavariables::system::variables_tag>,
       typename Metavariables::system::variables_tag,
@@ -409,7 +409,8 @@ struct component {
                                     Frame::ElementLogical, Frame::Inertial>,
       evolution::dg::Tags::Quadrature,
       domain::Tags::NeighborMesh<Metavariables::volume_dim>>;
-  using compute_tags = tmpl::list<
+  using compute_tags = tmpl::push_back<
+      time_stepper_ref_tags<LtsTimeStepper>,
       domain::Tags::JacobianCompute<Metavariables::volume_dim,
                                     Frame::ElementLogical, Frame::Inertial>,
       domain::Tags::DetInvJacobianCompute<
diff --git a/tests/Unit/Evolution/Initialization/Test_Evolution.cpp b/tests/Unit/Evolution/Initialization/Test_Evolution.cpp
index ca9a489397b7..d5945b20d49b 100644
--- a/tests/Unit/Evolution/Initialization/Test_Evolution.cpp
+++ b/tests/Unit/Evolution/Initialization/Test_Evolution.cpp
@@ -54,7 +54,7 @@ struct TestMetavariables {
   };
   using component_list = tmpl::list<>;
   using const_global_cache_tags =
-      tmpl::list<::Tags::TimeStepper<TimeStepperType>>;
+      tmpl::list<::Tags::ConcreteTimeStepper<TimeStepperType>>;
 };
 
 void test_gts() {
@@ -72,7 +72,7 @@ void test_gts() {
   const TimeDelta expected_time_step = time.slab().duration();
   const TimeDelta expected_next_time_step = expected_time_step;
 
-  tuples::TaggedTuple<::Tags::TimeStepper<TimeStepper>>
+  tuples::TaggedTuple<::Tags::ConcreteTimeStepper<TimeStepper>>
       const_global_cache_items(std::move(time_stepper));
 
   Parallel::GlobalCache<TestMetavariables<TimeStepper>> global_cache(
@@ -84,13 +84,13 @@ void test_gts() {
           Initialization::Tags::InitialSlabSize<false>,
           ::Tags::Next<::Tags::TimeStepId>, ::Tags::TimeStep,
           ::Tags::Next<::Tags::TimeStep>>,
-      tmpl::list<
-          Parallel::Tags::FromGlobalCache<::Tags::TimeStepper<TimeStepper>>>>(
+      tmpl::list<Parallel::Tags::FromGlobalCache<
+          ::Tags::ConcreteTimeStepper<TimeStepper>>>>(
       &global_cache, initial_time, initial_dt, initial_slab_size, TimeStepId{},
       TimeDelta{}, TimeDelta{});
 
-  db::mutate_apply<
-      Initialization::TimeStepping<TestMetavariables<TimeStepper>, false>>(
+  db::mutate_apply<Initialization::TimeStepping<TestMetavariables<TimeStepper>,
+                                                TimeStepper>>(
       make_not_null(&box));
 
   CHECK(db::get<::Tags::Next<::Tags::TimeStepId>>(box) ==
@@ -116,7 +116,7 @@ void test_lts() {
   const TimeDelta expected_time_step = choose_lts_step_size(time, initial_dt);
   const TimeDelta expected_next_time_step = expected_time_step;
 
-  tuples::TaggedTuple<::Tags::TimeStepper<LtsTimeStepper>>
+  tuples::TaggedTuple<::Tags::ConcreteTimeStepper<LtsTimeStepper>>
       const_global_cache_items(std::move(lts_time_stepper));
 
   Parallel::GlobalCache<TestMetavariables<LtsTimeStepper>> global_cache(
@@ -130,13 +130,12 @@ void test_lts() {
           ::Tags::Next<::Tags::TimeStepId>, ::Tags::TimeStep,
           ::Tags::Next<::Tags::TimeStep>>,
       tmpl::list<Parallel::Tags::FromGlobalCache<
-          ::Tags::TimeStepper<LtsTimeStepper>>>>(
+          ::Tags::ConcreteTimeStepper<LtsTimeStepper>>>>(
       &global_cache, initial_time, initial_dt, initial_slab_size, TimeStepId{},
       TimeDelta{}, TimeDelta{});
 
-  db::mutate_apply<
-      Initialization::TimeStepping<TestMetavariables<LtsTimeStepper>, true>>(
-      make_not_null(&box));
+  db::mutate_apply<Initialization::TimeStepping<
+      TestMetavariables<LtsTimeStepper>, LtsTimeStepper>>(make_not_null(&box));
 
   CHECK(db::get<::Tags::Next<::Tags::TimeStepId>>(box) ==
         expected_next_time_step_id);
diff --git a/tests/Unit/Evolution/Systems/Cce/Test_OptionTags.cpp b/tests/Unit/Evolution/Systems/Cce/Test_OptionTags.cpp
index a8701e042f6d..878c7e300127 100644
--- a/tests/Unit/Evolution/Systems/Cce/Test_OptionTags.cpp
+++ b/tests/Unit/Evolution/Systems/Cce/Test_OptionTags.cpp
@@ -81,8 +81,8 @@ SPECTRE_TEST_CASE("Unit.Evolution.Systems.Cce.OptionTags", "[Unit][Cce]") {
   TestHelpers::db::test_simple_tag<Cce::Tags::OutputNoninertialNews>(
       "OutputNoninertialNews");
   TestHelpers::db::test_simple_tag<
-      Cce::Tags::CceEvolutionPrefix<::Tags::TimeStepper<TimeStepper>>>(
-      "TimeStepper");
+      Cce::Tags::CceEvolutionPrefix<::Tags::ConcreteTimeStepper<TimeStepper>>>(
+      "ConcreteTimeStepper");
 
   CHECK(
       TestHelpers::test_option_tag<Cce::OptionTags::BondiSachsOutputFilePrefix>(
diff --git a/tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/Test_ChangeSlabSize.cpp b/tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/Test_ChangeSlabSize.cpp
index 8b3758eb0887..d2f249934cf7 100644
--- a/tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/Test_ChangeSlabSize.cpp
+++ b/tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/Test_ChangeSlabSize.cpp
@@ -54,8 +54,8 @@ struct MockWorldtubeSingleton {
               db::AddSimpleTags<
                   ::Tags::TimeStepId, ::Tags::Next<::Tags::TimeStepId>,
                   ::Tags::TimeStep, ::Tags::Next<::Tags::TimeStep>,
-                  ::Tags::TimeStepper<TimeStepper>>,
-              db::AddComputeTags<>>>>,
+                  ::Tags::ConcreteTimeStepper<TimeStepper>>,
+              time_stepper_ref_tags<TimeStepper>>>>,
       Parallel::PhaseActions<Parallel::Phase::Testing,
                              tmpl::list<Actions::ChangeSlabSize>>>;
   using component_being_mocked = WorldtubeSingleton<Metavariables>;
diff --git a/tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/Test_InitializeEvolvedVariables.cpp b/tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/Test_InitializeEvolvedVariables.cpp
index a2d5c3affe8f..d1884faccfaa 100644
--- a/tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/Test_InitializeEvolvedVariables.cpp
+++ b/tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/Test_InitializeEvolvedVariables.cpp
@@ -24,10 +24,12 @@ SPECTRE_TEST_CASE(
   auto box = db::create<
       db::AddSimpleTags<variables_tag, dt_variables_tag,
                         ::Tags::HistoryEvolvedVariables<variables_tag>,
-                        ::Tags::TimeStepper<TimeSteppers::AdamsBashforth>>>(
+                        ::Tags::ConcreteTimeStepper<TimeStepper>>,
+      time_stepper_ref_tags<TimeStepper>>(
       variables_tag::type{}, dt_variables_tag::type{},
       TimeSteppers::History<variables_tag::type>{},
-      std::make_unique<TimeSteppers::AdamsBashforth>(4));
+      static_cast<std::unique_ptr<TimeStepper>>(
+          std::make_unique<TimeSteppers::AdamsBashforth>(4)));
 
   db::mutate_apply<Initialization::InitializeEvolvedVariables>(
       make_not_null(&box));
diff --git a/tests/Unit/Helpers/Evolution/DiscontinuousGalerkin/Actions/ComputeTimeDerivativeImpl.tpp b/tests/Unit/Helpers/Evolution/DiscontinuousGalerkin/Actions/ComputeTimeDerivativeImpl.tpp
index b6089a648553..4885a5aaf9b6 100644
--- a/tests/Unit/Helpers/Evolution/DiscontinuousGalerkin/Actions/ComputeTimeDerivativeImpl.tpp
+++ b/tests/Unit/Helpers/Evolution/DiscontinuousGalerkin/Actions/ComputeTimeDerivativeImpl.tpp
@@ -915,8 +915,9 @@ struct component {
       ::Tags::IsUsingTimeSteppingErrorControl,
       tmpl::conditional_t<
           Metavariables::local_time_stepping,
-          tmpl::list<::Tags::StepChoosers, ::Tags::TimeStepper<LtsTimeStepper>>,
-          tmpl::list<::Tags::TimeStepper<TimeStepper>>>>>;
+          tmpl::list<::Tags::StepChoosers,
+                     ::Tags::ConcreteTimeStepper<LtsTimeStepper>>,
+          tmpl::list<::Tags::ConcreteTimeStepper<TimeStepper>>>>>;
   using common_compute_tags = tmpl::list<
       domain::Tags::JacobianCompute<Metavariables::volume_dim,
                                     Frame::ElementLogical, Frame::Inertial>,
@@ -946,8 +947,9 @@ struct component {
           boundary_directions_interior,
           domain::Tags::InterfaceMesh<Metavariables::volume_dim>>,
       domain::Tags::Slice<internal_directions, Var1>,
-      domain::Tags::Slice<internal_directions,
-                          Var2<Metavariables::volume_dim>>>;
+      domain::Tags::Slice<internal_directions, Var2<Metavariables::volume_dim>>,
+      time_stepper_ref_tags<tmpl::conditional_t<
+          Metavariables::local_time_stepping, LtsTimeStepper, TimeStepper>>>;
   using compute_tags = tmpl::conditional_t<
       Metavariables::system::has_primitive_and_conservative_vars,
       tmpl::push_front<common_compute_tags,
diff --git a/tests/Unit/Time/Actions/Test_AdvanceTime.cpp b/tests/Unit/Time/Actions/Test_AdvanceTime.cpp
index f862baf908f2..04176a2f09b5 100644
--- a/tests/Unit/Time/Actions/Test_AdvanceTime.cpp
+++ b/tests/Unit/Time/Actions/Test_AdvanceTime.cpp
@@ -43,20 +43,22 @@ struct Component {
   using metavariables = Metavariables;
   using chare_type = ActionTesting::MockArrayChare;
   using array_index = int;
-  using const_global_cache_tags = tmpl::list<Tags::TimeStepper<TimeStepper>>;
+  using const_global_cache_tags =
+      tmpl::list<Tags::ConcreteTimeStepper<TimeStepper>>;
 
   using simple_tags =
       db::AddSimpleTags<Tags::TimeStepId, Tags::Next<Tags::TimeStepId>,
                         Tags::TimeStep, Tags::Next<Tags::TimeStep>, Tags::Time,
                         Tags::IsUsingTimeSteppingErrorControl,
                         Tags::AdaptiveSteppingDiagnostics>;
+  using compute_tags = time_stepper_ref_tags<TimeStepper>;
 
-  using phase_dependent_action_list =
-      tmpl::list<Parallel::PhaseActions<
-                     Parallel::Phase::Initialization,
-                     tmpl::list<ActionTesting::InitializeDataBox<simple_tags>>>,
-                 Parallel::PhaseActions<Parallel::Phase::Testing,
-                                        tmpl::list<Actions::AdvanceTime>>>;
+  using phase_dependent_action_list = tmpl::list<
+      Parallel::PhaseActions<Parallel::Phase::Initialization,
+                             tmpl::list<ActionTesting::InitializeDataBox<
+                                 simple_tags, compute_tags>>>,
+      Parallel::PhaseActions<Parallel::Phase::Testing,
+                             tmpl::list<Actions::AdvanceTime>>>;
 };
 
 struct Metavariables {
diff --git a/tests/Unit/Time/Actions/Test_ChangeSlabSize.cpp b/tests/Unit/Time/Actions/Test_ChangeSlabSize.cpp
index 486c9d7d5063..78852b6c01a1 100644
--- a/tests/Unit/Time/Actions/Test_ChangeSlabSize.cpp
+++ b/tests/Unit/Time/Actions/Test_ChangeSlabSize.cpp
@@ -60,18 +60,20 @@ struct Component {
   using chare_type = ActionTesting::MockArrayChare;
   using array_index = int;
 
-  using const_global_cache_tags = tmpl::list<Tags::TimeStepper<TimeStepper>>;
+  using const_global_cache_tags =
+      tmpl::list<Tags::ConcreteTimeStepper<TimeStepper>>;
 
   using simple_tags =
       tmpl::list<Tags::TimeStepId, Tags::Next<Tags::TimeStepId>, Tags::TimeStep,
                  Tags::Next<Tags::TimeStep>, Tags::HistoryEvolvedVariables<Var>,
                  Tags::AdaptiveSteppingDiagnostics>;
-  using phase_dependent_action_list =
-      tmpl::list<Parallel::PhaseActions<
-                     Parallel::Phase::Initialization,
-                     tmpl::list<ActionTesting::InitializeDataBox<simple_tags>>>,
-                 Parallel::PhaseActions<Parallel::Phase::Testing,
-                                        tmpl::list<Actions::ChangeSlabSize>>>;
+  using compute_tags = time_stepper_ref_tags<TimeStepper>;
+  using phase_dependent_action_list = tmpl::list<
+      Parallel::PhaseActions<Parallel::Phase::Initialization,
+                             tmpl::list<ActionTesting::InitializeDataBox<
+                                 simple_tags, compute_tags>>>,
+      Parallel::PhaseActions<Parallel::Phase::Testing,
+                             tmpl::list<Actions::ChangeSlabSize>>>;
 };
 }  // namespace
 
@@ -123,7 +125,7 @@ SPECTRE_TEST_CASE("Unit.Time.Actions.ChangeSlabSize", "[Unit][Time][Actions]") {
           *next_id = stepper.next_time_id(*id, *step);
           *diags = AdaptiveSteppingDiagnostics{1, 2, 3, 4, 5};
         },
-        make_not_null(&box), db::get<Tags::TimeStepper<>>(box));
+        make_not_null(&box), db::get<Tags::TimeStepper<TimeStepper>>(box));
 
     using ExpectedMessages =
         ChangeSlabSize_detail::NumberOfExpectedMessagesInbox;
@@ -135,7 +137,7 @@ SPECTRE_TEST_CASE("Unit.Time.Actions.ChangeSlabSize", "[Unit][Time][Actions]") {
       CHECK(db::get<Tags::TimeStepId>(box) == id);
       CHECK(db::get<Tags::TimeStep>(box) == get_step(id));
       CHECK(db::get<Tags::Next<Tags::TimeStepId>>(box) ==
-            db::get<Tags::TimeStepper<>>(box).next_time_id(
+            db::get<Tags::TimeStepper<TimeStepper>>(box).next_time_id(
                 db::get<Tags::TimeStepId>(box), db::get<Tags::TimeStep>(box)));
       CHECK(db::get<Tags::AdaptiveSteppingDiagnostics>(box) ==
             AdaptiveSteppingDiagnostics{1, 2 + changes, 3, 4, 5});
@@ -212,7 +214,7 @@ SPECTRE_TEST_CASE("Unit.Time.Actions.ChangeSlabSize", "[Unit][Time][Actions]") {
             *next_id = stepper.next_time_id(*id, step);
           },
           make_not_null(&box), db::get<Tags::TimeStep>(box),
-          db::get<Tags::TimeStepper<>>(box));
+          db::get<Tags::TimeStepper<TimeStepper>>(box));
       const TimeStepId initial_id = db::get<Tags::TimeStepId>(box);
       get<ExpectedMessages>(inboxes)[3].insert(ExpectedMessages::NoData{});
       get<ExpectedMessages>(inboxes)[4].insert(ExpectedMessages::NoData{});
@@ -245,7 +247,7 @@ SPECTRE_TEST_CASE("Unit.Time.Actions.ChangeSlabSize", "[Unit][Time][Actions]") {
             }
           },
           make_not_null(&box), db::get<Tags::TimeStep>(box),
-          db::get<Tags::TimeStepper<>>(box));
+          db::get<Tags::TimeStepper<TimeStepper>>(box));
       const TimeStepId initial_id = db::get<Tags::TimeStepId>(box);
       get<ExpectedMessages>(inboxes)[3].insert(ExpectedMessages::NoData{});
       get<ExpectedMessages>(inboxes)[4].insert(ExpectedMessages::NoData{});
diff --git a/tests/Unit/Time/Actions/Test_ChangeStepSize.cpp b/tests/Unit/Time/Actions/Test_ChangeStepSize.cpp
index 85b20dfe4312..415c5dc94b7e 100644
--- a/tests/Unit/Time/Actions/Test_ChangeStepSize.cpp
+++ b/tests/Unit/Time/Actions/Test_ChangeStepSize.cpp
@@ -84,17 +84,19 @@ struct Component {
   using metavariables = Metavariables;
   using chare_type = ActionTesting::MockArrayChare;
   using array_index = int;
-  using const_global_cache_tags = tmpl::list<Tags::TimeStepper<LtsTimeStepper>>;
+  using const_global_cache_tags =
+      tmpl::list<Tags::ConcreteTimeStepper<LtsTimeStepper>>;
   using simple_tags =
       tmpl::list<Tags::TimeStepId, Tags::Next<Tags::TimeStepId>, Tags::TimeStep,
                  Tags::Next<Tags::TimeStep>, ::Tags::StepChoosers,
                  Tags::IsUsingTimeSteppingErrorControl,
                  Tags::AdaptiveSteppingDiagnostics, history_tag,
                  typename System::variables_tag>;
+  using compute_tags = time_stepper_ref_tags<LtsTimeStepper>;
   using phase_dependent_action_list = tmpl::list<
-      Parallel::PhaseActions<
-          Parallel::Phase::Initialization,
-          tmpl::list<ActionTesting::InitializeDataBox<simple_tags>>>,
+      Parallel::PhaseActions<Parallel::Phase::Initialization,
+                             tmpl::list<ActionTesting::InitializeDataBox<
+                                 simple_tags, compute_tags>>>,
       Parallel::PhaseActions<
           Parallel::Phase::Testing,
           tmpl::list<Actions::ChangeStepSize<
diff --git a/tests/Unit/Time/Actions/Test_SelfStartActions.cpp b/tests/Unit/Time/Actions/Test_SelfStartActions.cpp
index 813defb0ca09..35f575dabd98 100644
--- a/tests/Unit/Time/Actions/Test_SelfStartActions.cpp
+++ b/tests/Unit/Time/Actions/Test_SelfStartActions.cpp
@@ -142,7 +142,8 @@ struct Component {
   using metavariables = Metavariables;
   using chare_type = ActionTesting::MockArrayChare;
   using array_index = int;
-  using const_global_cache_tags = tmpl::list<Tags::TimeStepper<TimeStepper>>;
+  using const_global_cache_tags =
+      tmpl::list<Tags::ConcreteTimeStepper<TimeStepper>>;
   using simple_tags = tmpl::flatten<db::AddSimpleTags<
       typename metavariables::system::variables_tag,
       typename metavariables::system::test_primitive_variables_tags,
@@ -155,7 +156,7 @@ struct Component {
       Tags::Next<Tags::TimeStep>, Tags::Time,
       Tags::IsUsingTimeSteppingErrorControl,
       Tags::AdaptiveSteppingDiagnostics>>;
-  using compute_tags = db::AddComputeTags<>;
+  using compute_tags = time_stepper_ref_tags<TimeStepper>;
 
   static constexpr bool has_primitives = Metavariables::has_primitives;
 
diff --git a/tests/Unit/Time/Actions/Test_UpdateU.cpp b/tests/Unit/Time/Actions/Test_UpdateU.cpp
index b7376da0f267..a6483b6670f2 100644
--- a/tests/Unit/Time/Actions/Test_UpdateU.cpp
+++ b/tests/Unit/Time/Actions/Test_UpdateU.cpp
@@ -67,15 +67,16 @@ struct Component {
   using array_index = int;
   using const_global_cache_tags = tmpl::list<>;
   using simple_tags =
-      tmpl::list<Tags::TimeStepper<TimeStepper>, Tags::TimeStep,
+      tmpl::list<Tags::ConcreteTimeStepper<TimeStepper>, Tags::TimeStep,
                  ::Tags::IsUsingTimeSteppingErrorControl, Var,
                  Tags::HistoryEvolvedVariables<Var>, AlternativeVar,
                  Tags::HistoryEvolvedVariables<AlternativeVar>>;
+  using compute_tags = time_stepper_ref_tags<TimeStepper>;
 
   using phase_dependent_action_list = tmpl::list<
-      Parallel::PhaseActions<
-          Parallel::Phase::Initialization,
-          tmpl::list<ActionTesting::InitializeDataBox<simple_tags>>>,
+      Parallel::PhaseActions<Parallel::Phase::Initialization,
+                             tmpl::list<ActionTesting::InitializeDataBox<
+                                 simple_tags, compute_tags>>>,
       Parallel::PhaseActions<Parallel::Phase::Testing,
                              tmpl::list<Actions::UpdateU<
                                  typename metavariables::system_for_test>>>>;
@@ -101,12 +102,14 @@ void test_integration() {
     return 2. * t - 2. * (y - t * t);
   };
 
-  auto box = db::create<db::AddSimpleTags<
-      Tags::TimeStepper<TimeSteppers::Rk3HesthavenSsp>, Tags::TimeStep,
-      ::Tags::IsUsingTimeSteppingErrorControl, Var, history_tag, AlternativeVar,
-      alternative_history_tag>>(
-      std::make_unique<TimeSteppers::Rk3HesthavenSsp>(), time_step, false, 1.,
-      typename history_tag::type{3}, 1.,
+  auto box = db::create<
+      db::AddSimpleTags<Tags::ConcreteTimeStepper<TimeStepper>, Tags::TimeStep,
+                        ::Tags::IsUsingTimeSteppingErrorControl, Var,
+                        history_tag, AlternativeVar, alternative_history_tag>,
+      time_stepper_ref_tags<TimeStepper>>(
+      static_cast<std::unique_ptr<TimeStepper>>(
+          std::make_unique<TimeSteppers::Rk3HesthavenSsp>()),
+      time_step, false, 1., typename history_tag::type{3}, 1.,
       typename alternative_history_tag::type{3});
 
   const std::array<Time, 3> substep_times{
@@ -180,13 +183,16 @@ void test_stepper_error() {
   const Slab slab(1., 3.);
   const TimeDelta time_step = slab.duration() / 2;
 
-  auto box = db::create<db::AddSimpleTags<
-      Tags::TimeStepper<TimeSteppers::Rk3HesthavenSsp>, Tags::TimeStep,
-      ::Tags::IsUsingTimeSteppingErrorControl, variables_tag, history_tag,
-      Tags::StepperError<variables_tag>,
-      Tags::PreviousStepperError<variables_tag>, Tags::StepperErrorUpdated>>(
-      std::make_unique<TimeSteppers::Rk3HesthavenSsp>(), time_step, true, 1.,
-      history_tag::type{3}, 1234.5, 1234.5, false);
+  auto box = db::create<
+      db::AddSimpleTags<Tags::ConcreteTimeStepper<TimeStepper>, Tags::TimeStep,
+                        ::Tags::IsUsingTimeSteppingErrorControl, variables_tag,
+                        history_tag, Tags::StepperError<variables_tag>,
+                        Tags::PreviousStepperError<variables_tag>,
+                        Tags::StepperErrorUpdated>,
+      time_stepper_ref_tags<TimeStepper>>(
+      static_cast<std::unique_ptr<TimeStepper>>(
+          std::make_unique<TimeSteppers::Rk3HesthavenSsp>()),
+      time_step, true, 1., history_tag::type{3}, 1234.5, 1234.5, false);
 
   const std::array<TimeDelta, 3> substep_offsets{
       {0 * slab.duration(), time_step, time_step / 2}};
diff --git a/tests/Unit/Time/StepChoosers/Test_Cfl.cpp b/tests/Unit/Time/StepChoosers/Test_Cfl.cpp
index 1ee581cb86f5..47b0bee7eb4e 100644
--- a/tests/Unit/Time/StepChoosers/Test_Cfl.cpp
+++ b/tests/Unit/Time/StepChoosers/Test_Cfl.cpp
@@ -86,10 +86,11 @@ std::pair<double, bool> get_suggestion(const size_t stepper_order,
       db::AddSimpleTags<
           Parallel::Tags::MetavariablesImpl<Metavariables>, CharacteristicSpeed,
           domain::Tags::Coordinates<dim, frame>, domain::Tags::Mesh<dim>,
-          Tags::TimeStepper<TimeStepper>>,
-      db::AddComputeTags<domain::Tags::MinimumGridSpacingCompute<dim, frame>,
-                         typename Metavariables::system::
-                             compute_largest_characteristic_speed>>(
+          Tags::ConcreteTimeStepper<TimeStepper>>,
+      tmpl::push_back<time_stepper_ref_tags<TimeStepper>,
+                      domain::Tags::MinimumGridSpacingCompute<dim, frame>,
+                      typename Metavariables::system::
+                          compute_largest_characteristic_speed>>(
       Metavariables{}, characteristic_speed,
       tnsr::I<DataVector, dim, frame>{{{coordinates}}},
       Mesh<dim>(coordinates.size(), Spectral::Basis::Legendre,
diff --git a/tests/Unit/Time/StepChoosers/Test_ElementSizeCfl.cpp b/tests/Unit/Time/StepChoosers/Test_ElementSizeCfl.cpp
index 9e2a68566267..01ae03cecfd2 100644
--- a/tests/Unit/Time/StepChoosers/Test_ElementSizeCfl.cpp
+++ b/tests/Unit/Time/StepChoosers/Test_ElementSizeCfl.cpp
@@ -77,14 +77,16 @@ std::pair<double, bool> get_suggestion(
     ElementMap<Dim, Frame::Grid>&& element_map) {
   auto box = db::create<
       db::AddSimpleTags<Parallel::Tags::MetavariablesImpl<Metavariables<Dim>>,
-                        CharacteristicSpeed, Tags::TimeStepper<TimeStepper>,
+                        CharacteristicSpeed,
+                        Tags::ConcreteTimeStepper<TimeStepper>,
                         domain::Tags::ElementMap<Dim, Frame::Grid>,
                         domain::CoordinateMaps::Tags::CoordinateMap<
                             Dim, Frame::Grid, Frame::Inertial>,
                         ::Tags::Time, domain::Tags::FunctionsOfTimeInitialize>,
-      db::AddComputeTags<domain::Tags::SizeOfElementCompute<Dim>,
-                         typename Metavariables<Dim>::system::
-                             compute_largest_characteristic_speed>>(
+      tmpl::push_back<time_stepper_ref_tags<TimeStepper>,
+                      domain::Tags::SizeOfElementCompute<Dim>,
+                      typename Metavariables<Dim>::system::
+                          compute_largest_characteristic_speed>>(
       Metavariables<Dim>{}, characteristic_speed,
       std::unique_ptr<TimeStepper>{
           std::make_unique<TimeSteppers::AdamsBashforth>(2)},
@@ -104,7 +106,7 @@ std::pair<double, bool> get_suggestion(
       Dim>::system::compute_largest_characteristic_speed>(box);
   const std::array<double, Dim> element_size =
       db::get<domain::Tags::SizeOfElement<Dim>>(box);
-  const auto& time_stepper = get<Tags::TimeStepper<>>(box);
+  const auto& time_stepper = get<Tags::TimeStepper<TimeStepper>>(box);
 
   const double current_step = std::numeric_limits<double>::infinity();
   const std::pair<double, bool> result =
diff --git a/tests/Unit/Time/StepChoosers/Test_ErrorControl.cpp b/tests/Unit/Time/StepChoosers/Test_ErrorControl.cpp
index aecb3e7452f3..3bf5b6dca664 100644
--- a/tests/Unit/Time/StepChoosers/Test_ErrorControl.cpp
+++ b/tests/Unit/Time/StepChoosers/Test_ErrorControl.cpp
@@ -108,20 +108,19 @@ std::pair<double, bool> get_suggestion(
   history.insert(TimeStepId{true, 0, {{0.0, 1.0}, {0, 1}}}, step_values,
                  0.1 * step_values);
   history.discard_value(TimeStepId{true, 0, {{0.0, 1.0}, {0, 1}}});
-  auto box =
-      db::create<db::AddSimpleTags<
-                     Parallel::Tags::MetavariablesImpl<Metavariables<true>>,
-                     Tags::HistoryEvolvedVariables<EvolvedVariablesTag>,
-                     Tags::StepperError<EvolvedVariablesTag>,
-                     Tags::PreviousStepperError<EvolvedVariablesTag>,
-                     Tags::StepperErrorUpdated, Tags::TimeStepper<TimeStepper>>,
-                 db::AddComputeTags<>>(
-          Metavariables<true>{}, history, error, previous_error,
-          false,
-          std::unique_ptr<TimeStepper>{
-              std::make_unique<TimeSteppers::AdamsBashforth>(stepper_order)});
+  auto box = db::create<
+      db::AddSimpleTags<Parallel::Tags::MetavariablesImpl<Metavariables<true>>,
+                        Tags::HistoryEvolvedVariables<EvolvedVariablesTag>,
+                        Tags::StepperError<EvolvedVariablesTag>,
+                        Tags::PreviousStepperError<EvolvedVariablesTag>,
+                        Tags::StepperErrorUpdated,
+                        Tags::ConcreteTimeStepper<TimeStepper>>,
+      time_stepper_ref_tags<TimeStepper>>(
+      Metavariables<true>{}, history, error, previous_error, false,
+      std::unique_ptr<TimeStepper>{
+          std::make_unique<TimeSteppers::AdamsBashforth>(stepper_order)});
 
-  const auto& time_stepper = get<Tags::TimeStepper<>>(box);
+  const auto& time_stepper = get<Tags::TimeStepper<TimeStepper>>(box);
   const std::unique_ptr<StepChooser<StepChooserUse::LtsStep>>
       error_control_base = std::make_unique<LtsErrorControl>(error_control);
 
diff --git a/tests/Unit/Time/Tags/Test_TimeStepper.cpp b/tests/Unit/Time/Tags/Test_TimeStepper.cpp
index 2e97c22bee93..c366c2a2f82b 100644
--- a/tests/Unit/Time/Tags/Test_TimeStepper.cpp
+++ b/tests/Unit/Time/Tags/Test_TimeStepper.cpp
@@ -10,9 +10,34 @@
 
 namespace {
 struct DummyType {};
+
+class FakeTimeStepper {
+ public:
+  using provided_time_stepper_interfaces = tmpl::list<FakeTimeStepper>;
+};
+
+class MoreSpecificFakeTimeStepper : public FakeTimeStepper {
+ public:
+  using provided_time_stepper_interfaces =
+      tmpl::list<MoreSpecificFakeTimeStepper, FakeTimeStepper>;
+};
+
+static_assert(
+    std::is_same_v<
+        time_stepper_ref_tags<FakeTimeStepper>,
+        tmpl::list<Tags::TimeStepperRef<FakeTimeStepper, FakeTimeStepper>>>);
+static_assert(std::is_same_v<
+              time_stepper_ref_tags<MoreSpecificFakeTimeStepper>,
+              tmpl::list<Tags::TimeStepperRef<MoreSpecificFakeTimeStepper,
+                                              MoreSpecificFakeTimeStepper>,
+                         Tags::TimeStepperRef<FakeTimeStepper,
+                                              MoreSpecificFakeTimeStepper>>>);
 }  // namespace
 
 SPECTRE_TEST_CASE("Unit.Time.Tags.TimeStepper", "[Unit][Time]") {
-  TestHelpers::db::test_base_tag<Tags::TimeStepper<>>("TimeStepper");
+  TestHelpers::db::test_simple_tag<Tags::ConcreteTimeStepper<DummyType>>(
+      "ConcreteTimeStepper");
   TestHelpers::db::test_simple_tag<Tags::TimeStepper<DummyType>>("TimeStepper");
+  TestHelpers::db::test_reference_tag<
+      Tags::TimeStepperRef<DummyType, DummyType>>("TimeStepper");
 }
diff --git a/tests/Unit/Time/Test_ChangeSlabSize.cpp b/tests/Unit/Time/Test_ChangeSlabSize.cpp
index 4ed45239dda2..2d22614bc7e9 100644
--- a/tests/Unit/Time/Test_ChangeSlabSize.cpp
+++ b/tests/Unit/Time/Test_ChangeSlabSize.cpp
@@ -48,13 +48,16 @@ SPECTRE_TEST_CASE("Unit.Time.ChangeSlabSize", "[Unit][Time]") {
     TimeSteppers::History<Vars2::type> history2{};
     history2.insert(initial_id, 1.23, 4.56);
 
-    auto box = db::create<db::AddSimpleTags<
-        Tags::TimeStepper<TimeSteppers::AdamsBashforth>, Tags::TimeStepId,
-        Tags::TimeStep, Tags::Next<Tags::TimeStepId>,
-        Tags::Next<Tags::TimeStep>, Tags::AdaptiveSteppingDiagnostics,
-        Tags::HistoryEvolvedVariables<Vars1>,
-        Tags::HistoryEvolvedVariables<Vars2>>>(
-        std::make_unique<TimeSteppers::AdamsBashforth>(time_stepper),
+    auto box = db::create<
+        db::AddSimpleTags<
+            Tags::ConcreteTimeStepper<TimeStepper>, Tags::TimeStepId,
+            Tags::TimeStep, Tags::Next<Tags::TimeStepId>,
+            Tags::Next<Tags::TimeStep>, Tags::AdaptiveSteppingDiagnostics,
+            Tags::HistoryEvolvedVariables<Vars1>,
+            Tags::HistoryEvolvedVariables<Vars2>>,
+        time_stepper_ref_tags<TimeStepper>>(
+        static_cast<std::unique_ptr<TimeStepper>>(
+            std::make_unique<TimeSteppers::AdamsBashforth>(time_stepper)),
         initial_id, initial_step, next_id, next_step, diagnostics,
         std::move(history1), std::move(history2));
 
@@ -98,13 +101,16 @@ SPECTRE_TEST_CASE("Unit.Time.ChangeSlabSize", "[Unit][Time]") {
     TimeSteppers::History<Vars2::type> history2{};
     history2.insert(initial_id, 1.23, 4.56);
 
-    auto box = db::create<db::AddSimpleTags<
-        Tags::TimeStepper<TimeSteppers::Rk3HesthavenSsp>, Tags::TimeStepId,
-        Tags::TimeStep, Tags::Next<Tags::TimeStepId>,
-        Tags::Next<Tags::TimeStep>, Tags::AdaptiveSteppingDiagnostics,
-        Tags::HistoryEvolvedVariables<Vars1>,
-        Tags::HistoryEvolvedVariables<Vars2>>>(
-        std::make_unique<TimeSteppers::Rk3HesthavenSsp>(time_stepper),
+    auto box = db::create<
+        db::AddSimpleTags<
+            Tags::ConcreteTimeStepper<TimeStepper>, Tags::TimeStepId,
+            Tags::TimeStep, Tags::Next<Tags::TimeStepId>,
+            Tags::Next<Tags::TimeStep>, Tags::AdaptiveSteppingDiagnostics,
+            Tags::HistoryEvolvedVariables<Vars1>,
+            Tags::HistoryEvolvedVariables<Vars2>>,
+        time_stepper_ref_tags<TimeStepper>>(
+        static_cast<std::unique_ptr<TimeStepper>>(
+            std::make_unique<TimeSteppers::Rk3HesthavenSsp>(time_stepper)),
         initial_id, initial_step, next_id, next_step, diagnostics,
         std::move(history1), std::move(history2));
 
@@ -148,13 +154,16 @@ SPECTRE_TEST_CASE("Unit.Time.ChangeSlabSize", "[Unit][Time]") {
     TimeSteppers::History<Vars2::type> history2{};
     history2.insert(initial_id, 1.23, 4.56);
 
-    auto box = db::create<db::AddSimpleTags<
-        Tags::TimeStepper<TimeSteppers::AdamsBashforth>, Tags::TimeStepId,
-        Tags::TimeStep, Tags::Next<Tags::TimeStepId>,
-        Tags::Next<Tags::TimeStep>, Tags::AdaptiveSteppingDiagnostics,
-        Tags::HistoryEvolvedVariables<Vars1>,
-        Tags::HistoryEvolvedVariables<Vars2>>>(
-        std::make_unique<TimeSteppers::AdamsBashforth>(time_stepper),
+    auto box = db::create<
+        db::AddSimpleTags<
+            Tags::ConcreteTimeStepper<TimeStepper>, Tags::TimeStepId,
+            Tags::TimeStep, Tags::Next<Tags::TimeStepId>,
+            Tags::Next<Tags::TimeStep>, Tags::AdaptiveSteppingDiagnostics,
+            Tags::HistoryEvolvedVariables<Vars1>,
+            Tags::HistoryEvolvedVariables<Vars2>>,
+        time_stepper_ref_tags<TimeStepper>>(
+        static_cast<std::unique_ptr<TimeStepper>>(
+            std::make_unique<TimeSteppers::AdamsBashforth>(time_stepper)),
         initial_id, initial_step, next_id, next_step, diagnostics, history1,
         history2);
 
diff --git a/tests/Unit/Time/Test_TakeStep.cpp b/tests/Unit/Time/Test_TakeStep.cpp
index 51d29ca7442a..aa42f1960b14 100644
--- a/tests/Unit/Time/Test_TakeStep.cpp
+++ b/tests/Unit/Time/Test_TakeStep.cpp
@@ -102,13 +102,15 @@ void test_gts() {
       },
       [](const auto y, const auto /*t*/) { return 1.0e-2 * y; }, time_step, 4);
 
-  auto box = db::create<db::AddSimpleTags<
-      Parallel::Tags::MetavariablesImpl<Metavariables>, Tags::TimeStepId,
-      Tags::Next<Tags::TimeStepId>, Tags::TimeStep, Tags::Next<Tags::TimeStep>,
-      EvolvedVariable, Tags::dt<EvolvedVariable>,
-      Tags::HistoryEvolvedVariables<EvolvedVariable>,
-      Tags::TimeStepper<TimeStepper>,
-      ::Tags::IsUsingTimeSteppingErrorControl>>(
+  auto box = db::create<
+      db::AddSimpleTags<Parallel::Tags::MetavariablesImpl<Metavariables>,
+                        Tags::TimeStepId, Tags::Next<Tags::TimeStepId>,
+                        Tags::TimeStep, Tags::Next<Tags::TimeStep>,
+                        EvolvedVariable, Tags::dt<EvolvedVariable>,
+                        Tags::HistoryEvolvedVariables<EvolvedVariable>,
+                        Tags::ConcreteTimeStepper<TimeStepper>,
+                        ::Tags::IsUsingTimeSteppingErrorControl>,
+      time_stepper_ref_tags<TimeStepper>>(
       Metavariables{}, TimeStepId{true, 0_st, slab.start()},
       TimeStepId{true, 0_st, Time{slab, {1, 4}}}, time_step, time_step,
       initial_values, DataVector{5, 0.0}, std::move(history),
@@ -170,12 +172,13 @@ void test_lts() {
           Tags::dt<EvolvedVariable>, Tags::StepperError<EvolvedVariable>,
           Tags::PreviousStepperError<EvolvedVariable>,
           Tags::HistoryEvolvedVariables<EvolvedVariable>,
-          Tags::TimeStepper<LtsTimeStepper>, Tags::StepChoosers,
+          Tags::ConcreteTimeStepper<LtsTimeStepper>, Tags::StepChoosers,
           domain::Tags::MinimumGridSpacing<1, Frame::Inertial>,
           ::Tags::IsUsingTimeSteppingErrorControl, Tags::StepperErrorUpdated,
           Tags::AdaptiveSteppingDiagnostics>,
-      db::AddComputeTags<typename Metavariables::system::
-                             compute_largest_characteristic_speed>>(
+      tmpl::push_back<time_stepper_ref_tags<LtsTimeStepper>,
+                      typename Metavariables::system::
+                          compute_largest_characteristic_speed>>(
       Metavariables{}, TimeStepId{true, 0_st, slab.start()},
       TimeStepId{true, 0_st, Time{slab, {1, 4}}}, time_step, time_step,
       initial_values, DataVector{5, 0.0}, DataVector{}, DataVector{},
@@ -219,7 +222,7 @@ void test_lts() {
         *next_time_step =
             local_time_step->with_slab(next_time_id->step_time().slab());
       },
-      make_not_null(&box), db::get<Tags::TimeStepper<>>(box));
+      make_not_null(&box), db::get<Tags::TimeStepper<LtsTimeStepper>>(box));
 
   db::mutate<Tags::dt<EvolvedVariable>>(update_rhs, make_not_null(&box),
                                         db::get<EvolvedVariable>(box));