diff --git a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/normalizer/NormalizeCTEIds.scala b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/normalizer/NormalizeCTEIds.scala
index 6c0bca0e1104f..17fd9486ad9aa 100644
--- a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/normalizer/NormalizeCTEIds.scala
+++ b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/normalizer/NormalizeCTEIds.scala
@@ -21,6 +21,7 @@ import java.util.concurrent.atomic.AtomicLong
 
 import scala.collection.mutable
 
+import org.apache.spark.sql.catalyst.expressions.SubqueryExpression
 import org.apache.spark.sql.catalyst.plans.logical.{CacheTableAsSelect, CTERelationRef, LogicalPlan, UnionLoop, UnionLoopRef, WithCTE}
 import org.apache.spark.sql.catalyst.rules.Rule
 
@@ -53,7 +54,7 @@ object NormalizeCTEIds extends Rule[LogicalPlan] {
   private def canonicalizeCTE(
       plan: LogicalPlan,
       defIdToNewId: mutable.Map[Long, Long]): LogicalPlan = {
-    plan.transformDownWithSubqueries {
+    val normalizedPlan = plan match {
       // For nested WithCTE, if defIndex didn't contain the cteId,
       // means it's not current WithCTE's ref.
       case ref: CTERelationRef if defIdToNewId.contains(ref.cteId) =>
@@ -62,6 +63,17 @@ object NormalizeCTEIds extends Rule[LogicalPlan] {
         unionLoop.copy(id = defIdToNewId(unionLoop.id))
       case unionLoopRef: UnionLoopRef if defIdToNewId.contains(unionLoopRef.loopId) =>
         unionLoopRef.copy(loopId = defIdToNewId(unionLoopRef.loopId))
+      case other => other
     }
+
+    normalizedPlan
+      .withNewChildren(normalizedPlan.children.map {
+        case withCTE: WithCTE => withCTE
+        case child => canonicalizeCTE(child, defIdToNewId)
+      })
+      .transformExpressionsDown {
+        case subqueryExpression: SubqueryExpression =>
+          subqueryExpression.withNewPlan(canonicalizeCTE(subqueryExpression.plan, defIdToNewId))
+      }
   }
 }
diff --git a/sql/core/src/test/scala/org/apache/spark/sql/CTEInlineSuite.scala b/sql/core/src/test/scala/org/apache/spark/sql/CTEInlineSuite.scala
index 7562d5669cc2c..1371e59545fdf 100644
--- a/sql/core/src/test/scala/org/apache/spark/sql/CTEInlineSuite.scala
+++ b/sql/core/src/test/scala/org/apache/spark/sql/CTEInlineSuite.scala
@@ -261,6 +261,45 @@ abstract class CTEInlineSuiteBase
     }
   }
 
+  test("SPARK-56921: plan normalization handles nested CTEs under union") {
+    withTempView("input", "common") {
+      Seq((1, 1, 10), (1, 2, 20), (2, 1, 30))
+        .toDF("a", "b", "value")
+        .createOrReplaceTempView("input")
+
+      sql(
+        s"""with cte_common as (
+           |  select a, b, sum(value) as value
+           |  from input
+           |  group by a, b
+           |)
+           |select * from cte_common
+         """.stripMargin).createOrReplaceTempView("common")
+
+      val left = sql(
+        s"""with cte_a as (
+           |  select a, sum(value) as value
+           |  from common
+           |  group by a
+           |)
+           |select a as id, value from cte_a
+         """.stripMargin)
+
+      val right = sql(
+        s"""with cte_b as (
+           |  select b, sum(value) as value
+           |  from common
+           |  group by b
+           |)
+           |select b as id, value from cte_b
+         """.stripMargin)
+
+      val df = left.union(right)
+      df.queryExecution.normalized
+      checkAnswer(df, Row(1, 30) :: Row(2, 30) :: Row(1, 40) :: Row(2, 20) :: Nil)
+    }
+  }
+
   test("SPARK-36447: invalid nested CTEs") {
     withTempView("t") {
       Seq((0, 1), (1, 2)).toDF("c1", "c2").createOrReplaceTempView("t")