diff --git a/core/src/main/kotlin/org/jetbrains/kotlinx/dataframe/api/add.kt b/core/src/main/kotlin/org/jetbrains/kotlinx/dataframe/api/add.kt
index 16033ee92a..050d8a7499 100644
--- a/core/src/main/kotlin/org/jetbrains/kotlinx/dataframe/api/add.kt
+++ b/core/src/main/kotlin/org/jetbrains/kotlinx/dataframe/api/add.kt
@@ -225,6 +225,7 @@ public class AddDsl<T>(
     @AccessApiOverload
     public fun group(column: AnyColumnGroupAccessor, body: AddDsl<T>.() -> Unit): Unit = group(column.name(), body)
 
+    @Interpretable("AddDslNamedGroup")
     public fun group(name: String, body: AddDsl<T>.() -> Unit) {
         val dsl = AddDsl(df)
         body(dsl)
diff --git a/core/src/main/kotlin/org/jetbrains/kotlinx/dataframe/api/insert.kt b/core/src/main/kotlin/org/jetbrains/kotlinx/dataframe/api/insert.kt
index 61f3b59e68..03efde6593 100644
--- a/core/src/main/kotlin/org/jetbrains/kotlinx/dataframe/api/insert.kt
+++ b/core/src/main/kotlin/org/jetbrains/kotlinx/dataframe/api/insert.kt
@@ -83,6 +83,7 @@ public fun <T> InsertClause<T>.after(column: ColumnSelector<T, *>): DataFrame<T>
 
 public fun <T> InsertClause<T>.after(column: String): DataFrame<T> = df.add(this.column).move(this.column).after(column)
 
+@AccessApiOverload
 public fun <T> InsertClause<T>.after(column: ColumnAccessor<*>): DataFrame<T> = after(column.path())
 
 @AccessApiOverload
diff --git a/core/src/main/kotlin/org/jetbrains/kotlinx/dataframe/api/move.kt b/core/src/main/kotlin/org/jetbrains/kotlinx/dataframe/api/move.kt
index 8e549c6ba7..5095e1c579 100644
--- a/core/src/main/kotlin/org/jetbrains/kotlinx/dataframe/api/move.kt
+++ b/core/src/main/kotlin/org/jetbrains/kotlinx/dataframe/api/move.kt
@@ -53,10 +53,13 @@ public fun <T> DataFrame<T>.moveTo(newColumnIndex: Int, vararg columns: KPropert
 
 // region moveToLeft
 
+@Refine
+@Interpretable("MoveToLeft1")
 public fun <T> DataFrame<T>.moveToLeft(columns: ColumnsSelector<T, *>): DataFrame<T> = move(columns).toLeft()
 
 public fun <T> DataFrame<T>.moveToLeft(vararg columns: String): DataFrame<T> = moveToLeft { columns.toColumnSet() }
 
+@AccessApiOverload
 public fun <T> DataFrame<T>.moveToLeft(vararg columns: AnyColumnReference): DataFrame<T> =
     moveToLeft { columns.toColumnSet() }
 
@@ -68,13 +71,17 @@ public fun <T> DataFrame<T>.moveToLeft(vararg columns: KProperty<*>): DataFrame<
 
 // region moveToRight
 
+@Refine
+@Interpretable("MoveToRight1")
 public fun <T> DataFrame<T>.moveToRight(columns: ColumnsSelector<T, *>): DataFrame<T> = move(columns).toRight()
 
 public fun <T> DataFrame<T>.moveToRight(vararg columns: String): DataFrame<T> = moveToRight { columns.toColumnSet() }
 
+@AccessApiOverload
 public fun <T> DataFrame<T>.moveToRight(vararg columns: AnyColumnReference): DataFrame<T> =
     moveToRight { columns.toColumnSet() }
 
+@AccessApiOverload
 public fun <T> DataFrame<T>.moveToRight(vararg columns: KProperty<*>): DataFrame<T> =
     moveToRight { columns.toColumnSet() }
 
@@ -94,6 +101,11 @@ public fun <T, C> MoveClause<T, C>.into(
         newPathExpression = column,
     )
 
+/**
+ * Move a single selected column to top level with a new name
+ */
+@Refine
+@Interpretable("MoveInto0")
 public fun <T, C> MoveClause<T, C>.into(column: String): DataFrame<T> = pathOf(column).let { path -> into { path } }
 
 public fun <T, C> MoveClause<T, C>.intoIndexed(
@@ -109,11 +121,19 @@ public fun <T, C> MoveClause<T, C>.intoIndexed(
 
 // region under
 
+@Refine
+@Interpretable("MoveUnder0")
 public fun <T, C> MoveClause<T, C>.under(column: String): DataFrame<T> = pathOf(column).let { path -> under { path } }
 
+@AccessApiOverload
 public fun <T, C> MoveClause<T, C>.under(column: AnyColumnGroupAccessor): DataFrame<T> =
     column.path().let { path -> under { path } }
 
+/**
+ * Move selected columns under existing column group
+ */
+@Refine
+@Interpretable("MoveUnder1")
 public fun <T, C> MoveClause<T, C>.under(
     column: ColumnsSelectionDsl<T>.(ColumnWithPath<C>) -> AnyColumnReference,
 ): DataFrame<T> =
@@ -138,10 +158,13 @@ public fun <T, C> MoveClause<T, C>.toTop(
 
 // region after
 
+@Refine
+@Interpretable("MoveAfter0")
 public fun <T, C> MoveClause<T, C>.after(column: ColumnSelector<T, *>): DataFrame<T> = afterOrBefore(column, true)
 
 public fun <T, C> MoveClause<T, C>.after(column: String): DataFrame<T> = after { column.toColumnAccessor() }
 
+@AccessApiOverload
 public fun <T, C> MoveClause<T, C>.after(column: AnyColumnReference): DataFrame<T> = after { column }
 
 @AccessApiOverload
@@ -157,8 +180,12 @@ fun <T, C> MoveColsClause<T, C>.before(column: String) = before { column.toColum
 fun <T, C> MoveColsClause<T, C>.before(column: ColumnSelector<T, *>) = afterOrBefore(column, false)
 */
 
+@Refine
+@Interpretable("MoveToLeft0")
 public fun <T, C> MoveClause<T, C>.toLeft(): DataFrame<T> = to(0)
 
+@Refine
+@Interpretable("MoveToRight0")
 public fun <T, C> MoveClause<T, C>.toRight(): DataFrame<T> = to(df.ncol)
 
 public class MoveClause<T, C>(internal val df: DataFrame<T>, internal val columns: ColumnsSelector<T, C>) {
diff --git a/core/src/main/kotlin/org/jetbrains/kotlinx/dataframe/api/toDataFrame.kt b/core/src/main/kotlin/org/jetbrains/kotlinx/dataframe/api/toDataFrame.kt
index b26eaf36a9..6c81fc73fc 100644
--- a/core/src/main/kotlin/org/jetbrains/kotlinx/dataframe/api/toDataFrame.kt
+++ b/core/src/main/kotlin/org/jetbrains/kotlinx/dataframe/api/toDataFrame.kt
@@ -202,6 +202,7 @@ public abstract class CreateDataFrameDsl<T> : TraversePropertiesDsl {
 
     public inline fun <reified R> inferType(noinline expression: (T) -> R): InferType<T, R> = InferType(expression)
 
+    @Interpretable("ToDataFrameDslStringInvoke")
     public abstract operator fun String.invoke(builder: CreateDataFrameDsl<T>.() -> Unit)
 }
 
diff --git a/core/src/test/kotlin/org/jetbrains/kotlinx/dataframe/testSets/person/DataFrameTreeTests.kt b/core/src/test/kotlin/org/jetbrains/kotlinx/dataframe/testSets/person/DataFrameTreeTests.kt
index adbae4bcc4..f84bdea9f9 100644
--- a/core/src/test/kotlin/org/jetbrains/kotlinx/dataframe/testSets/person/DataFrameTreeTests.kt
+++ b/core/src/test/kotlin/org/jetbrains/kotlinx/dataframe/testSets/person/DataFrameTreeTests.kt
@@ -795,4 +795,10 @@ class DataFrameTreeTests : BaseTest() {
         val df = typed2.convert { nameAndCity }.asFrame { it.remove { city } }
         df.nameAndCity.columns() shouldBe typed2.nameAndCity.remove { city }.columns()
     }
+
+    @Test
+    fun `move under existing group`() {
+        val df = typed2.move { age }.under { nameAndCity }
+        df.nameAndCity.columnNames() shouldBe listOf("name", "city", "age")
+    }
 }
diff --git a/plugins/kotlin-dataframe/src/org/jetbrains/kotlinx/dataframe/plugin/impl/api/add.kt b/plugins/kotlin-dataframe/src/org/jetbrains/kotlinx/dataframe/plugin/impl/api/add.kt
index 9b908edc59..19a66ee8a0 100644
--- a/plugins/kotlin-dataframe/src/org/jetbrains/kotlinx/dataframe/plugin/impl/api/add.kt
+++ b/plugins/kotlin-dataframe/src/org/jetbrains/kotlinx/dataframe/plugin/impl/api/add.kt
@@ -68,3 +68,15 @@ class AddDslStringInvoke : AbstractInterpreter<Unit>() {
         dsl.columns.add(SimpleColumnGroup(receiver, addDsl.columns))
     }
 }
+
+class AddDslNamedGroup : AbstractInterpreter<Unit>() {
+    val Arguments.dsl: AddDslApproximation by arg()
+    val Arguments.name: String by arg()
+    val Arguments.body by dsl()
+
+    override fun Arguments.interpret() {
+        val addDsl = AddDslApproximation(mutableListOf())
+        body(addDsl, emptyMap())
+        dsl.columns.add(SimpleColumnGroup(name, addDsl.columns))
+    }
+}
diff --git a/plugins/kotlin-dataframe/src/org/jetbrains/kotlinx/dataframe/plugin/impl/api/move.kt b/plugins/kotlin-dataframe/src/org/jetbrains/kotlinx/dataframe/plugin/impl/api/move.kt
index d9c9b824e1..90c7db09dd 100644
--- a/plugins/kotlin-dataframe/src/org/jetbrains/kotlinx/dataframe/plugin/impl/api/move.kt
+++ b/plugins/kotlin-dataframe/src/org/jetbrains/kotlinx/dataframe/plugin/impl/api/move.kt
@@ -1,8 +1,13 @@
 package org.jetbrains.kotlinx.dataframe.plugin.impl.api
 
+import org.jetbrains.kotlinx.dataframe.api.after
+import org.jetbrains.kotlinx.dataframe.api.into
 import org.jetbrains.kotlinx.dataframe.api.move
-import org.jetbrains.kotlinx.dataframe.api.pathOf
+import org.jetbrains.kotlinx.dataframe.api.moveToLeft
+import org.jetbrains.kotlinx.dataframe.api.toLeft
+import org.jetbrains.kotlinx.dataframe.api.toRight
 import org.jetbrains.kotlinx.dataframe.api.toTop
+import org.jetbrains.kotlinx.dataframe.api.under
 import org.jetbrains.kotlinx.dataframe.columns.toColumnSet
 import org.jetbrains.kotlinx.dataframe.plugin.impl.AbstractInterpreter
 import org.jetbrains.kotlinx.dataframe.plugin.impl.AbstractSchemaModificationInterpreter
@@ -30,4 +35,74 @@ class ToTop : AbstractSchemaModificationInterpreter() {
     }
 }
 
+class MoveUnder0 : AbstractSchemaModificationInterpreter() {
+    val Arguments.receiver: MoveClauseApproximation by arg()
+    val Arguments.column: String by arg()
+
+    override fun Arguments.interpret(): PluginDataFrameSchema {
+        val columns = receiver.columns.resolve(receiver.df).map { it.path }
+        return receiver.df.asDataFrame().move { columns.toColumnSet() }.under(column).toPluginDataFrameSchema()
+    }
+}
+
+class MoveUnder1 : AbstractSchemaModificationInterpreter() {
+    val Arguments.receiver: MoveClauseApproximation by arg()
+    val Arguments.column: SingleColumnApproximation by arg()
+
+    override fun Arguments.interpret(): PluginDataFrameSchema {
+        val columns = receiver.columns.resolve(receiver.df).map { it.path }
+        return receiver.df.asDataFrame().move { columns.toColumnSet() }.under { column.col.path }.toPluginDataFrameSchema()
+    }
+}
+
+class MoveInto0 : AbstractSchemaModificationInterpreter() {
+    val Arguments.receiver: MoveClauseApproximation by arg()
+    val Arguments.column: String by arg()
+
+    override fun Arguments.interpret(): PluginDataFrameSchema {
+        val columns = receiver.columns.resolve(receiver.df).map { it.path }
+        return receiver.df.asDataFrame().move { columns.toColumnSet() }.into(column).toPluginDataFrameSchema()
+    }
+}
+
+class MoveToLeft0 : AbstractSchemaModificationInterpreter() {
+    val Arguments.receiver: MoveClauseApproximation by arg()
+
+    override fun Arguments.interpret(): PluginDataFrameSchema {
+        val columns = receiver.columns.resolve(receiver.df).map { it.path }
+        return receiver.df.asDataFrame().move { columns.toColumnSet() }.toLeft().toPluginDataFrameSchema()
+    }
+}
+
+class MoveToLeft1 : AbstractSchemaModificationInterpreter() {
+    val Arguments.receiver: PluginDataFrameSchema by dataFrame()
+    val Arguments.columns: ColumnsResolver by arg()
+
+    override fun Arguments.interpret(): PluginDataFrameSchema {
+        val columns = columns.resolve(receiver).map { it.path }
+        return receiver.asDataFrame().moveToLeft { columns.toColumnSet() }.toPluginDataFrameSchema()
+    }
+}
+
+
+class MoveToRight0 : AbstractSchemaModificationInterpreter() {
+    val Arguments.receiver: MoveClauseApproximation by arg()
+
+    override fun Arguments.interpret(): PluginDataFrameSchema {
+        val columns = receiver.columns.resolve(receiver.df).map { it.path }
+        return receiver.df.asDataFrame().move { columns.toColumnSet() }.toRight().toPluginDataFrameSchema()
+    }
+}
+
+class MoveAfter0 : AbstractSchemaModificationInterpreter() {
+    val Arguments.receiver: MoveClauseApproximation by arg()
+    val Arguments.column: SingleColumnApproximation by arg()
+
+    override fun Arguments.interpret(): PluginDataFrameSchema {
+        val columns = receiver.columns.resolve(receiver.df).map { it.path }
+        return receiver.df.asDataFrame().move { columns.toColumnSet() }.after { column.col.path }.toPluginDataFrameSchema()
+    }
+}
+
+
 class MoveClauseApproximation(val df: PluginDataFrameSchema, val columns: ColumnsResolver)
diff --git a/plugins/kotlin-dataframe/src/org/jetbrains/kotlinx/dataframe/plugin/impl/api/toDataFrame.kt b/plugins/kotlin-dataframe/src/org/jetbrains/kotlinx/dataframe/plugin/impl/api/toDataFrame.kt
index 60fb38b76a..4b632b80f0 100644
--- a/plugins/kotlin-dataframe/src/org/jetbrains/kotlinx/dataframe/plugin/impl/api/toDataFrame.kt
+++ b/plugins/kotlin-dataframe/src/org/jetbrains/kotlinx/dataframe/plugin/impl/api/toDataFrame.kt
@@ -131,6 +131,18 @@ class Properties0 : AbstractInterpreter<Unit>() {
     }
 }
 
+class ToDataFrameDslStringInvoke : AbstractInterpreter<Unit>() {
+    val Arguments.dsl: CreateDataFrameDslImplApproximation by arg()
+    val Arguments.receiver: String by arg()
+    val Arguments.builder by dsl()
+
+    override fun Arguments.interpret() {
+        val addDsl = CreateDataFrameDslImplApproximation()
+        builder(addDsl, emptyMap())
+        dsl.columns.add(SimpleColumnGroup(receiver, addDsl.columns))
+    }
+}
+
 class CreateDataFrameConfiguration {
     var maxDepth = DEFAULT_MAX_DEPTH
     var traverseConfiguration: TraverseConfiguration = TraverseConfiguration()
diff --git a/plugins/kotlin-dataframe/src/org/jetbrains/kotlinx/dataframe/plugin/loadInterpreter.kt b/plugins/kotlin-dataframe/src/org/jetbrains/kotlinx/dataframe/plugin/loadInterpreter.kt
index 7e583707f0..33f642992d 100644
--- a/plugins/kotlin-dataframe/src/org/jetbrains/kotlinx/dataframe/plugin/loadInterpreter.kt
+++ b/plugins/kotlin-dataframe/src/org/jetbrains/kotlinx/dataframe/plugin/loadInterpreter.kt
@@ -71,6 +71,7 @@ import org.jetbrains.kotlin.name.CallableId
 import org.jetbrains.kotlin.name.ClassId
 import org.jetbrains.kotlin.name.Name
 import org.jetbrains.kotlin.name.StandardClassIds
+import org.jetbrains.kotlinx.dataframe.plugin.impl.api.AddDslNamedGroup
 import org.jetbrains.kotlinx.dataframe.plugin.impl.api.AddDslStringInvoke
 import org.jetbrains.kotlinx.dataframe.plugin.impl.api.AddId
 import org.jetbrains.kotlinx.dataframe.plugin.impl.api.Aggregate
@@ -88,6 +89,13 @@ import org.jetbrains.kotlinx.dataframe.plugin.impl.api.FlattenDefault
 import org.jetbrains.kotlinx.dataframe.plugin.impl.api.FrameCols0
 import org.jetbrains.kotlinx.dataframe.plugin.impl.api.MapToFrame
 import org.jetbrains.kotlinx.dataframe.plugin.impl.api.Move0
+import org.jetbrains.kotlinx.dataframe.plugin.impl.api.MoveAfter0
+import org.jetbrains.kotlinx.dataframe.plugin.impl.api.MoveInto0
+import org.jetbrains.kotlinx.dataframe.plugin.impl.api.MoveToLeft0
+import org.jetbrains.kotlinx.dataframe.plugin.impl.api.MoveToLeft1
+import org.jetbrains.kotlinx.dataframe.plugin.impl.api.MoveToRight0
+import org.jetbrains.kotlinx.dataframe.plugin.impl.api.MoveUnder0
+import org.jetbrains.kotlinx.dataframe.plugin.impl.api.MoveUnder1
 import org.jetbrains.kotlinx.dataframe.plugin.impl.api.PairConstructor
 import org.jetbrains.kotlinx.dataframe.plugin.impl.api.PairToConstructor
 import org.jetbrains.kotlinx.dataframe.plugin.impl.api.ReadExcel
@@ -96,6 +104,7 @@ import org.jetbrains.kotlinx.dataframe.plugin.impl.api.ToDataFrame
 import org.jetbrains.kotlinx.dataframe.plugin.impl.api.ToDataFrameColumn
 import org.jetbrains.kotlinx.dataframe.plugin.impl.api.ToDataFrameDefault
 import org.jetbrains.kotlinx.dataframe.plugin.impl.api.ToDataFrameDsl
+import org.jetbrains.kotlinx.dataframe.plugin.impl.api.ToDataFrameDslStringInvoke
 import org.jetbrains.kotlinx.dataframe.plugin.impl.api.ToDataFrameFrom
 import org.jetbrains.kotlinx.dataframe.plugin.impl.api.ToTop
 import org.jetbrains.kotlinx.dataframe.plugin.impl.api.TrimMargin
@@ -235,6 +244,7 @@ internal inline fun <reified T> String.load(): T {
         "toDataFrameDsl" -> ToDataFrameDsl()
         "toDataFrame" -> ToDataFrame()
         "toDataFrameDefault" -> ToDataFrameDefault()
+        "ToDataFrameDslStringInvoke" -> ToDataFrameDslStringInvoke()
         "DataFrameOf0" -> DataFrameOf0()
         "DataFrameBuilderInvoke0" -> DataFrameBuilderInvoke0()
         "ToDataFrameColumn" -> ToDataFrameColumn()
@@ -246,6 +256,7 @@ internal inline fun <reified T> String.load(): T {
         "FlattenDefault" -> FlattenDefault()
         "AddId" -> AddId()
         "AddDslStringInvoke" -> AddDslStringInvoke()
+        "AddDslNamedGroup" -> AddDslNamedGroup()
         "MapToFrame" -> MapToFrame()
         "Move0" -> Move0()
         "ToTop" -> ToTop()
@@ -255,6 +266,13 @@ internal inline fun <reified T> String.load(): T {
         "ValueCounts" -> ValueCounts()
         "RenameToCamelCase" -> RenameToCamelCase()
         "RenameToCamelCaseClause" -> RenameToCamelCaseClause()
+        "MoveUnder0" -> MoveUnder0()
+        "MoveUnder1" -> MoveUnder1()
+        "MoveInto0" -> MoveInto0()
+        "MoveToLeft0" -> MoveToLeft0()
+        "MoveToLeft1" -> MoveToLeft1()
+        "MoveToRight0" -> MoveToRight0()
+        "MoveAfter0" -> MoveAfter0()
         else -> error("$this")
     } as T
 }
diff --git a/plugins/kotlin-dataframe/testData/box/addDsl.kt b/plugins/kotlin-dataframe/testData/box/addDsl.kt
index 2cc4cb84f8..0b91151b53 100644
--- a/plugins/kotlin-dataframe/testData/box/addDsl.kt
+++ b/plugins/kotlin-dataframe/testData/box/addDsl.kt
@@ -9,8 +9,12 @@ fun box(): String {
         "group" {
             "a" from { it }
         }
+        group("group1") {
+            "b" from { it }
+        }
     }
 
     df.group.a
+    df.group1.b
     return "OK"
 }
diff --git a/plugins/kotlin-dataframe/testData/box/moveAfter.fir.txt b/plugins/kotlin-dataframe/testData/box/moveAfter.fir.txt
new file mode 100644
index 0000000000..55361cd60d
--- /dev/null
+++ b/plugins/kotlin-dataframe/testData/box/moveAfter.fir.txt
@@ -0,0 +1,107 @@
+FILE: moveAfter.kt
+    public final fun box(): R|kotlin/String| {
+        lval df: R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_66>| = R|org/jetbrains/kotlinx/dataframe/api/dataFrameOf|(vararg(String(a), String(b), String(c))).R|kotlin/let|<R|org/jetbrains/kotlinx/dataframe/api/DataFrameBuilder|, R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_64>|>(<L> = fun <anonymous>(it: R|org/jetbrains/kotlinx/dataframe/api/DataFrameBuilder|): R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_64>| <inline=Inline, kind=EXACTLY_ONCE>  {
+            local abstract class Invoke_64I : R|kotlin/Any| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(2)) public abstract val c: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(1)) public abstract val b: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(0)) public abstract val a: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                public constructor(): R|<local>/Invoke_64I|
+
+            }
+
+            local final class Scope0 : R|kotlin/Any| {
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_64I>|.c: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_64I>|.c: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_64I>|.b: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_64I>|.b: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_64I>|.a: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_64I>|.a: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+
+                public constructor(): R|<local>/Scope0|
+
+            }
+
+            local abstract class Invoke_64 : R|<local>/Invoke_64I| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/ScopeProperty|() public abstract val scope0: R|<local>/Scope0|
+                    public get(): R|<local>/Scope0|
+
+                public constructor(): R|<local>/Invoke_64|
+
+            }
+
+            ^ R|<local>/it|.R|org/jetbrains/kotlinx/dataframe/api/DataFrameBuilder.invoke|(vararg(Int(1), Int(2), Int(3)))
+        }
+        ).R|org/jetbrains/kotlinx/dataframe/api/move|<R|<local>/Invoke_64|, R|kotlin/Int|>(<L> = move@fun R|org/jetbrains/kotlinx/dataframe/api/ColumnsSelectionDsl<<local>/Invoke_64>|.<anonymous>(it: R|org/jetbrains/kotlinx/dataframe/api/ColumnsSelectionDsl<<local>/Invoke_64>|): R|org/jetbrains/kotlinx/dataframe/columns/ColumnsResolver<kotlin/Int>| <inline=NoInline>  {
+            ^ (this@R|/box|, this@R|special/anonymous|).R|<local>/Scope0.a|
+        }
+        ).R|kotlin/let|<R|org/jetbrains/kotlinx/dataframe/api/MoveClause<<local>/Invoke_64, kotlin/Int>|, R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_66>|>(<L> = fun <anonymous>(it: R|org/jetbrains/kotlinx/dataframe/api/MoveClause<<local>/Invoke_64, kotlin/Int>|): R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_66>| <inline=Inline, kind=EXACTLY_ONCE>  {
+            local abstract class Invoke_66I : R|kotlin/Any| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(2)) public abstract val c: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(0)) public abstract val b: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(1)) public abstract val a: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                public constructor(): R|<local>/Invoke_66I|
+
+            }
+
+            local final class Scope0 : R|kotlin/Any| {
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_66I>|.c: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_66I>|.c: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_66I>|.b: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_66I>|.b: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_66I>|.a: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_66I>|.a: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+
+                public constructor(): R|<local>/Scope0|
+
+            }
+
+            local abstract class Invoke_66 : R|<local>/Invoke_66I| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/ScopeProperty|() public abstract val scope0: R|<local>/Scope0|
+                    public get(): R|<local>/Scope0|
+
+                public constructor(): R|<local>/Invoke_66|
+
+            }
+
+            ^ R|<local>/it|.R|org/jetbrains/kotlinx/dataframe/api/after|<R|<local>/Invoke_64|, R|kotlin/Int|>(<L> = after@fun R|org/jetbrains/kotlinx/dataframe/api/ColumnsSelectionDsl<<local>/Invoke_64>|.<anonymous>(it: R|org/jetbrains/kotlinx/dataframe/api/ColumnsSelectionDsl<<local>/Invoke_64>|): R|org/jetbrains/kotlinx/dataframe/columns/SingleColumn<*>| <inline=NoInline>  {
+                ^ (this@R|/box|, this@R|special/anonymous|).R|<local>/Scope0.b|
+            }
+            )
+        }
+        )
+        ^box String(OK)
+    }
diff --git a/plugins/kotlin-dataframe/testData/box/moveAfter.kt b/plugins/kotlin-dataframe/testData/box/moveAfter.kt
new file mode 100644
index 0000000000..9b5df0e106
--- /dev/null
+++ b/plugins/kotlin-dataframe/testData/box/moveAfter.kt
@@ -0,0 +1,10 @@
+// FIR_DUMP
+import org.jetbrains.kotlinx.dataframe.*
+import org.jetbrains.kotlinx.dataframe.annotations.*
+import org.jetbrains.kotlinx.dataframe.api.*
+import org.jetbrains.kotlinx.dataframe.io.*
+
+fun box(): String {
+    val df = dataFrameOf("a", "b", "c")(1, 2, 3).move { a }.after { b }
+    return "OK"
+}
diff --git a/plugins/kotlin-dataframe/testData/box/moveInto.kt b/plugins/kotlin-dataframe/testData/box/moveInto.kt
new file mode 100644
index 0000000000..2d6e9f4219
--- /dev/null
+++ b/plugins/kotlin-dataframe/testData/box/moveInto.kt
@@ -0,0 +1,13 @@
+import org.jetbrains.kotlinx.dataframe.*
+import org.jetbrains.kotlinx.dataframe.annotations.*
+import org.jetbrains.kotlinx.dataframe.api.*
+import org.jetbrains.kotlinx.dataframe.io.*
+
+fun box(): String {
+    val df = dataFrameOf("a", "b", "c")(1, 2, 3)
+        .group { a and b }.into("d")
+        .move { d.a }.into("renamedA")
+    df.renamedA
+    df.compareSchemas(strict = true)
+    return "OK"
+}
diff --git a/plugins/kotlin-dataframe/testData/box/moveToLeft.fir.txt b/plugins/kotlin-dataframe/testData/box/moveToLeft.fir.txt
new file mode 100644
index 0000000000..cf3b43a6b7
--- /dev/null
+++ b/plugins/kotlin-dataframe/testData/box/moveToLeft.fir.txt
@@ -0,0 +1,234 @@
+FILE: moveToLeft.kt
+    public final fun box(): R|kotlin/String| {
+        lval df: R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_83>| = R|org/jetbrains/kotlinx/dataframe/api/dataFrameOf|(vararg(String(s))).R|kotlin/let|<R|org/jetbrains/kotlinx/dataframe/api/DataFrameBuilder|, R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_56>|>(<L> = fun <anonymous>(it: R|org/jetbrains/kotlinx/dataframe/api/DataFrameBuilder|): R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_56>| <inline=Inline, kind=EXACTLY_ONCE>  {
+            local abstract class Invoke_56I : R|kotlin/Any| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(0)) public abstract val s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public constructor(): R|<local>/Invoke_56I|
+
+            }
+
+            local final class Scope0 : R|kotlin/Any| {
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_56I>|.s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_56I>|.s: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+
+                public constructor(): R|<local>/Scope0|
+
+            }
+
+            local abstract class Invoke_56 : R|<local>/Invoke_56I| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/ScopeProperty|() public abstract val scope0: R|<local>/Scope0|
+                    public get(): R|<local>/Scope0|
+
+                public constructor(): R|<local>/Invoke_56|
+
+            }
+
+            ^ R|<local>/it|.R|org/jetbrains/kotlinx/dataframe/api/DataFrameBuilder.invoke|(vararg(String(str)))
+        }
+        ).R|kotlin/let|<R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_56>|, R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_68>|>(<L> = fun <anonymous>(it: R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_56>|): R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_68>| <inline=Inline, kind=EXACTLY_ONCE>  {
+            local abstract class Invoke_68I : R|kotlin/Any| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(1)) public abstract val l: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(0)) public abstract val s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public constructor(): R|<local>/Invoke_68I|
+
+            }
+
+            local final class Scope0 : R|kotlin/Any| {
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_68I>|.l: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_68I>|.l: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_68I>|.s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_68I>|.s: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+
+                public constructor(): R|<local>/Scope0|
+
+            }
+
+            local abstract class Invoke_68 : R|<local>/Invoke_68I| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/ScopeProperty|() public abstract val scope0: R|<local>/Scope0|
+                    public get(): R|<local>/Scope0|
+
+                public constructor(): R|<local>/Invoke_68|
+
+            }
+
+            ^ R|<local>/it|.R|org/jetbrains/kotlinx/dataframe/api/add|<R|kotlin/Int|, R|<local>/Invoke_56|>(String(l), <L> = add@fun R|org/jetbrains/kotlinx/dataframe/api/AddDataRow<<local>/Invoke_56>|.<anonymous>(it: R|org/jetbrains/kotlinx/dataframe/api/AddDataRow<<local>/Invoke_56>|): R|kotlin/Int| <inline=NoInline>  {
+                ^ (this@R|/box|, this@R|special/anonymous|).R|<local>/Scope0.s|.R|kotlin/String.length|
+            }
+            )
+        }
+        ).R|org/jetbrains/kotlinx/dataframe/api/move|<R|<local>/Invoke_68|, R|kotlin/Int|>(<L> = move@fun R|org/jetbrains/kotlinx/dataframe/api/ColumnsSelectionDsl<<local>/Invoke_68>|.<anonymous>(it: R|org/jetbrains/kotlinx/dataframe/api/ColumnsSelectionDsl<<local>/Invoke_68>|): R|org/jetbrains/kotlinx/dataframe/columns/ColumnsResolver<kotlin/Int>| <inline=NoInline>  {
+            ^ (this@R|/box|, this@R|special/anonymous|).R|<local>/Scope0.l|
+        }
+        ).R|kotlin/let|<R|org/jetbrains/kotlinx/dataframe/api/MoveClause<<local>/Invoke_68, kotlin/Int>|, R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_83>|>(<L> = fun <anonymous>(it: R|org/jetbrains/kotlinx/dataframe/api/MoveClause<<local>/Invoke_68, kotlin/Int>|): R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_83>| <inline=Inline, kind=EXACTLY_ONCE>  {
+            local abstract class Invoke_83I : R|kotlin/Any| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(0)) public abstract val l: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(1)) public abstract val s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public constructor(): R|<local>/Invoke_83I|
+
+            }
+
+            local final class Scope0 : R|kotlin/Any| {
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_83I>|.l: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_83I>|.l: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_83I>|.s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_83I>|.s: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+
+                public constructor(): R|<local>/Scope0|
+
+            }
+
+            local abstract class Invoke_83 : R|<local>/Invoke_83I| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/ScopeProperty|() public abstract val scope0: R|<local>/Scope0|
+                    public get(): R|<local>/Scope0|
+
+                public constructor(): R|<local>/Invoke_83|
+
+            }
+
+            ^ R|<local>/it|.R|org/jetbrains/kotlinx/dataframe/api/toLeft|<R|<local>/Invoke_68|, R|kotlin/Int|>()
+        }
+        )
+        lval df1: R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_97>| = R|org/jetbrains/kotlinx/dataframe/api/dataFrameOf|(vararg(String(s))).R|kotlin/let|<R|org/jetbrains/kotlinx/dataframe/api/DataFrameBuilder|, R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_56>|>(<L> = fun <anonymous>(it: R|org/jetbrains/kotlinx/dataframe/api/DataFrameBuilder|): R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_56>| <inline=Inline, kind=EXACTLY_ONCE>  {
+            local abstract class Invoke_56I : R|kotlin/Any| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(0)) public abstract val s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public constructor(): R|<local>/Invoke_56I|
+
+            }
+
+            local final class Scope0 : R|kotlin/Any| {
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_56I>|.s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_56I>|.s: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+
+                public constructor(): R|<local>/Scope0|
+
+            }
+
+            local abstract class Invoke_56 : R|<local>/Invoke_56I| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/ScopeProperty|() public abstract val scope0: R|<local>/Scope0|
+                    public get(): R|<local>/Scope0|
+
+                public constructor(): R|<local>/Invoke_56|
+
+            }
+
+            ^ R|<local>/it|.R|org/jetbrains/kotlinx/dataframe/api/DataFrameBuilder.invoke|(vararg(String(str)))
+        }
+        ).R|kotlin/let|<R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_56>|, R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_68>|>(<L> = fun <anonymous>(it: R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_56>|): R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_68>| <inline=Inline, kind=EXACTLY_ONCE>  {
+            local abstract class Invoke_68I : R|kotlin/Any| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(1)) public abstract val l: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(0)) public abstract val s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public constructor(): R|<local>/Invoke_68I|
+
+            }
+
+            local final class Scope0 : R|kotlin/Any| {
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_68I>|.l: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_68I>|.l: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_68I>|.s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_68I>|.s: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+
+                public constructor(): R|<local>/Scope0|
+
+            }
+
+            local abstract class Invoke_68 : R|<local>/Invoke_68I| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/ScopeProperty|() public abstract val scope0: R|<local>/Scope0|
+                    public get(): R|<local>/Scope0|
+
+                public constructor(): R|<local>/Invoke_68|
+
+            }
+
+            ^ R|<local>/it|.R|org/jetbrains/kotlinx/dataframe/api/add|<R|kotlin/Int|, R|<local>/Invoke_56|>(String(l), <L> = add@fun R|org/jetbrains/kotlinx/dataframe/api/AddDataRow<<local>/Invoke_56>|.<anonymous>(it: R|org/jetbrains/kotlinx/dataframe/api/AddDataRow<<local>/Invoke_56>|): R|kotlin/Int| <inline=NoInline>  {
+                ^ (this@R|/box|, this@R|special/anonymous|).R|<local>/Scope0.s|.R|kotlin/String.length|
+            }
+            )
+        }
+        ).R|kotlin/let|<R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_68>|, R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_97>|>(<L> = fun <anonymous>(it: R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_68>|): R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_97>| <inline=Inline, kind=EXACTLY_ONCE>  {
+            local abstract class Invoke_97I : R|kotlin/Any| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(0)) public abstract val l: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(1)) public abstract val s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public constructor(): R|<local>/Invoke_97I|
+
+            }
+
+            local final class Scope0 : R|kotlin/Any| {
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_97I>|.l: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_97I>|.l: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_97I>|.s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_97I>|.s: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+
+                public constructor(): R|<local>/Scope0|
+
+            }
+
+            local abstract class Invoke_97 : R|<local>/Invoke_97I| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/ScopeProperty|() public abstract val scope0: R|<local>/Scope0|
+                    public get(): R|<local>/Scope0|
+
+                public constructor(): R|<local>/Invoke_97|
+
+            }
+
+            ^ R|<local>/it|.R|org/jetbrains/kotlinx/dataframe/api/moveToLeft|<R|<local>/Invoke_68|>(<L> = moveToLeft@fun R|org/jetbrains/kotlinx/dataframe/api/ColumnsSelectionDsl<<local>/Invoke_68>|.<anonymous>(it: R|org/jetbrains/kotlinx/dataframe/api/ColumnsSelectionDsl<<local>/Invoke_68>|): R|org/jetbrains/kotlinx/dataframe/columns/ColumnsResolver<*>| <inline=NoInline>  {
+                ^ (this@R|/box|, this@R|special/anonymous|).R|<local>/Scope0.l|
+            }
+            )
+        }
+        )
+        ^box String(OK)
+    }
diff --git a/plugins/kotlin-dataframe/testData/box/moveToLeft.kt b/plugins/kotlin-dataframe/testData/box/moveToLeft.kt
new file mode 100644
index 0000000000..066a51e95e
--- /dev/null
+++ b/plugins/kotlin-dataframe/testData/box/moveToLeft.kt
@@ -0,0 +1,11 @@
+// FIR_DUMP
+import org.jetbrains.kotlinx.dataframe.*
+import org.jetbrains.kotlinx.dataframe.annotations.*
+import org.jetbrains.kotlinx.dataframe.api.*
+import org.jetbrains.kotlinx.dataframe.io.*
+
+fun box(): String {
+    val df = dataFrameOf("s")("str").add("l") { s.length }.move { l }.toLeft()
+    val df1 = dataFrameOf("s")("str").add("l") { s.length }.moveToLeft { l }
+    return "OK"
+}
diff --git a/plugins/kotlin-dataframe/testData/box/moveToRight.fir.txt b/plugins/kotlin-dataframe/testData/box/moveToRight.fir.txt
new file mode 100644
index 0000000000..83dfcc3897
--- /dev/null
+++ b/plugins/kotlin-dataframe/testData/box/moveToRight.fir.txt
@@ -0,0 +1,116 @@
+FILE: moveToRight.kt
+    public final fun box(): R|kotlin/String| {
+        lval df: R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_56>| = R|org/jetbrains/kotlinx/dataframe/api/dataFrameOf|(vararg(String(s))).R|kotlin/let|<R|org/jetbrains/kotlinx/dataframe/api/DataFrameBuilder|, R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_56>|>(<L> = fun <anonymous>(it: R|org/jetbrains/kotlinx/dataframe/api/DataFrameBuilder|): R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_56>| <inline=Inline, kind=EXACTLY_ONCE>  {
+            local abstract class Invoke_56I : R|kotlin/Any| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(0)) public abstract val s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public constructor(): R|<local>/Invoke_56I|
+
+            }
+
+            local final class Scope0 : R|kotlin/Any| {
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_56I>|.s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_56I>|.s: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+
+                public constructor(): R|<local>/Scope0|
+
+            }
+
+            local abstract class Invoke_56 : R|<local>/Invoke_56I| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/ScopeProperty|() public abstract val scope0: R|<local>/Scope0|
+                    public get(): R|<local>/Scope0|
+
+                public constructor(): R|<local>/Invoke_56|
+
+            }
+
+            ^ R|<local>/it|.R|org/jetbrains/kotlinx/dataframe/api/DataFrameBuilder.invoke|(vararg(String(str)))
+        }
+        ).R|kotlin/let|<R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_56>|, R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_69>|>(<L> = fun <anonymous>(it: R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_56>|): R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_69>| <inline=Inline, kind=EXACTLY_ONCE>  {
+            local abstract class Invoke_69I : R|kotlin/Any| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(0)) public abstract val id: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(1)) public abstract val s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public constructor(): R|<local>/Invoke_69I|
+
+            }
+
+            local final class Scope0 : R|kotlin/Any| {
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_69I>|.id: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_69I>|.id: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_69I>|.s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_69I>|.s: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+
+                public constructor(): R|<local>/Scope0|
+
+            }
+
+            local abstract class Invoke_69 : R|<local>/Invoke_69I| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/ScopeProperty|() public abstract val scope0: R|<local>/Scope0|
+                    public get(): R|<local>/Scope0|
+
+                public constructor(): R|<local>/Invoke_69|
+
+            }
+
+            ^ R|<local>/it|.R|org/jetbrains/kotlinx/dataframe/api/addId|<R|<local>/Invoke_56|>()
+        }
+        ).R|org/jetbrains/kotlinx/dataframe/api/move|<R|<local>/Invoke_69|, R|kotlin/Int|>(<L> = move@fun R|org/jetbrains/kotlinx/dataframe/api/ColumnsSelectionDsl<<local>/Invoke_69>|.<anonymous>(it: R|org/jetbrains/kotlinx/dataframe/api/ColumnsSelectionDsl<<local>/Invoke_69>|): R|org/jetbrains/kotlinx/dataframe/columns/ColumnsResolver<kotlin/Int>| <inline=NoInline>  {
+            ^ (this@R|/box|, this@R|special/anonymous|).R|<local>/Scope0.id|
+        }
+        ).R|kotlin/let|<R|org/jetbrains/kotlinx/dataframe/api/MoveClause<<local>/Invoke_69, kotlin/Int>|, R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_56>|>(<L> = fun <anonymous>(it: R|org/jetbrains/kotlinx/dataframe/api/MoveClause<<local>/Invoke_69, kotlin/Int>|): R|org/jetbrains/kotlinx/dataframe/DataFrame<<local>/Invoke_56>| <inline=Inline, kind=EXACTLY_ONCE>  {
+            local abstract class Invoke_56I : R|kotlin/Any| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(1)) public abstract val id: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                @R|org/jetbrains/kotlinx/dataframe/annotations/Order|(order = Int(0)) public abstract val s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public constructor(): R|<local>/Invoke_56I|
+
+            }
+
+            local final class Scope0 : R|kotlin/Any| {
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_56I>|.id: R|kotlin/Int|
+                    public get(): R|kotlin/Int|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_56I>|.id: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/Int>|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/DataRow<<local>/Invoke_56I>|.s: R|kotlin/String|
+                    public get(): R|kotlin/String|
+
+                public final val R|org/jetbrains/kotlinx/dataframe/ColumnsScope<<local>/Invoke_56I>|.s: R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+                    public get(): R|org/jetbrains/kotlinx/dataframe/DataColumn<kotlin/String>|
+
+                public constructor(): R|<local>/Scope0|
+
+            }
+
+            local abstract class Invoke_56 : R|<local>/Invoke_56I| {
+                @R|org/jetbrains/kotlinx/dataframe/annotations/ScopeProperty|() public abstract val scope0: R|<local>/Scope0|
+                    public get(): R|<local>/Scope0|
+
+                public constructor(): R|<local>/Invoke_56|
+
+            }
+
+            ^ R|<local>/it|.R|org/jetbrains/kotlinx/dataframe/api/toRight|<R|<local>/Invoke_69|, R|kotlin/Int|>()
+        }
+        )
+        ^box String(OK)
+    }
diff --git a/plugins/kotlin-dataframe/testData/box/moveToRight.kt b/plugins/kotlin-dataframe/testData/box/moveToRight.kt
new file mode 100644
index 0000000000..444125a085
--- /dev/null
+++ b/plugins/kotlin-dataframe/testData/box/moveToRight.kt
@@ -0,0 +1,10 @@
+// FIR_DUMP
+import org.jetbrains.kotlinx.dataframe.*
+import org.jetbrains.kotlinx.dataframe.annotations.*
+import org.jetbrains.kotlinx.dataframe.api.*
+import org.jetbrains.kotlinx.dataframe.io.*
+
+fun box(): String {
+    val df = dataFrameOf("s")("str").addId().move { id }.toRight()
+    return "OK"
+}
diff --git a/plugins/kotlin-dataframe/testData/box/moveUnder.kt b/plugins/kotlin-dataframe/testData/box/moveUnder.kt
new file mode 100644
index 0000000000..8d4f0a9d3a
--- /dev/null
+++ b/plugins/kotlin-dataframe/testData/box/moveUnder.kt
@@ -0,0 +1,17 @@
+import org.jetbrains.kotlinx.dataframe.*
+import org.jetbrains.kotlinx.dataframe.annotations.*
+import org.jetbrains.kotlinx.dataframe.api.*
+import org.jetbrains.kotlinx.dataframe.io.*
+
+fun box(): String {
+    val df = dataFrameOf("a", "b", "c")(1, 2, 3)
+        .group { a and b }.into("d")
+        .move { c }.under { d }
+    df.compareSchemas(strict = true)
+
+    // alias for group into
+    dataFrameOf("a", "b", "c")(1, 2, 3)
+        .move { a and b }.under("d")
+        .compareSchemas(strict = true)
+    return "OK"
+}
diff --git a/plugins/kotlin-dataframe/testData/box/toDataFrame_nested.kt b/plugins/kotlin-dataframe/testData/box/toDataFrame_nested.kt
new file mode 100644
index 0000000000..34409a1699
--- /dev/null
+++ b/plugins/kotlin-dataframe/testData/box/toDataFrame_nested.kt
@@ -0,0 +1,19 @@
+import org.jetbrains.kotlinx.dataframe.*
+import org.jetbrains.kotlinx.dataframe.annotations.*
+import org.jetbrains.kotlinx.dataframe.api.*
+import org.jetbrains.kotlinx.dataframe.io.*
+
+fun box(): String {
+    val df = listOf("a").toDataFrame {
+        "group" {
+            "anotherGroup" {
+                "a" from { 1 }
+            }
+            "b" from { "c" }
+        }
+    }
+
+    df.group.b
+    df.group.anotherGroup.a
+    return "OK"
+}
diff --git a/plugins/kotlin-dataframe/tests-gen/org/jetbrains/kotlin/fir/dataframe/DataFrameBlackBoxCodegenTestGenerated.java b/plugins/kotlin-dataframe/tests-gen/org/jetbrains/kotlin/fir/dataframe/DataFrameBlackBoxCodegenTestGenerated.java
index ef62a062cf..d736fc4081 100644
--- a/plugins/kotlin-dataframe/tests-gen/org/jetbrains/kotlin/fir/dataframe/DataFrameBlackBoxCodegenTestGenerated.java
+++ b/plugins/kotlin-dataframe/tests-gen/org/jetbrains/kotlin/fir/dataframe/DataFrameBlackBoxCodegenTestGenerated.java
@@ -286,12 +286,42 @@ public void testMapToFrame() {
     runTest("testData/box/mapToFrame.kt");
   }
 
+  @Test
+  @TestMetadata("moveAfter.kt")
+  public void testMoveAfter() {
+    runTest("testData/box/moveAfter.kt");
+  }
+
+  @Test
+  @TestMetadata("moveInto.kt")
+  public void testMoveInto() {
+    runTest("testData/box/moveInto.kt");
+  }
+
+  @Test
+  @TestMetadata("moveToLeft.kt")
+  public void testMoveToLeft() {
+    runTest("testData/box/moveToLeft.kt");
+  }
+
+  @Test
+  @TestMetadata("moveToRight.kt")
+  public void testMoveToRight() {
+    runTest("testData/box/moveToRight.kt");
+  }
+
   @Test
   @TestMetadata("moveToTop.kt")
   public void testMoveToTop() {
     runTest("testData/box/moveToTop.kt");
   }
 
+  @Test
+  @TestMetadata("moveUnder.kt")
+  public void testMoveUnder() {
+    runTest("testData/box/moveUnder.kt");
+  }
+
   @Test
   @TestMetadata("nestedDataSchemaCodegen.kt")
   public void testNestedDataSchemaCodegen() {
@@ -478,6 +508,12 @@ public void testToDataFrame_from() {
     runTest("testData/box/toDataFrame_from.kt");
   }
 
+  @Test
+  @TestMetadata("toDataFrame_nested.kt")
+  public void testToDataFrame_nested() {
+    runTest("testData/box/toDataFrame_nested.kt");
+  }
+
   @Test
   @TestMetadata("toDataFrame_nullableList.kt")
   public void testToDataFrame_nullableList() {