diff --git a/akka-cluster-sharding-typed/src/main/mima-filters/2.6.5.backwards.excludes/daemon-process-init-overloads.excludes b/akka-cluster-sharding-typed/src/main/mima-filters/2.6.5.backwards.excludes/daemon-process-init-overloads.excludes
new file mode 100644
index 0000000000..5b607dd7f1
--- /dev/null
+++ b/akka-cluster-sharding-typed/src/main/mima-filters/2.6.5.backwards.excludes/daemon-process-init-overloads.excludes
@@ -0,0 +1,3 @@
+# Non-settings stop message overload for Sharded Daemon Process #29081
+ProblemFilters.exclude[ReversedMissingMethodProblem]("akka.cluster.sharding.typed.scaladsl.ShardedDaemonProcess.init")
+ProblemFilters.exclude[ReversedMissingMethodProblem]("akka.cluster.sharding.typed.javadsl.ShardedDaemonProcess.init")
\ No newline at end of file
diff --git a/akka-cluster-sharding-typed/src/main/scala/akka/cluster/sharding/typed/internal/ShardedDaemonProcessImpl.scala b/akka-cluster-sharding-typed/src/main/scala/akka/cluster/sharding/typed/internal/ShardedDaemonProcessImpl.scala
index 01233edf86..a5c12d66f1 100644
--- a/akka-cluster-sharding-typed/src/main/scala/akka/cluster/sharding/typed/internal/ShardedDaemonProcessImpl.scala
+++ b/akka-cluster-sharding-typed/src/main/scala/akka/cluster/sharding/typed/internal/ShardedDaemonProcessImpl.scala
@@ -93,9 +93,12 @@ private[akka] final class ShardedDaemonProcessImpl(system: ActorSystem[_])
   import ShardedDaemonProcessImpl._
 
   def init[T](name: String, numberOfInstances: Int, behaviorFactory: Int => Behavior[T])(
-      implicit classTag: ClassTag[T]): Unit = {
+      implicit classTag: ClassTag[T]): Unit =
     init(name, numberOfInstances, behaviorFactory, ShardedDaemonProcessSettings(system), None)(classTag)
-  }
+
+  override def init[T](name: String, numberOfInstances: Int, behaviorFactory: Int => Behavior[T], stopMessage: T)(
+      implicit classTag: ClassTag[T]): Unit =
+    init(name, numberOfInstances, behaviorFactory, ShardedDaemonProcessSettings(system), Some(stopMessage))(classTag)
 
   def init[T](
       name: String,
@@ -153,6 +156,7 @@ private[akka] final class ShardedDaemonProcessImpl(system: ActorSystem[_])
     }
   }
 
+  // Java API
   def init[T](
       messageClass: Class[T],
       name: String,
@@ -160,6 +164,15 @@ private[akka] final class ShardedDaemonProcessImpl(system: ActorSystem[_])
       behaviorFactory: function.Function[Integer, Behavior[T]]): Unit =
     init(name, numberOfInstances, n => behaviorFactory(n))(ClassTag(messageClass))
 
+  override def init[T](
+      messageClass: Class[T],
+      name: String,
+      numberOfInstances: Int,
+      behaviorFactory: function.Function[Int, Behavior[T]],
+      stopMessage: T): Unit =
+    init(name, numberOfInstances, n => behaviorFactory(n), ShardedDaemonProcessSettings(system), Some(stopMessage))(
+      ClassTag(messageClass))
+
   def init[T](
       messageClass: Class[T],
       name: String,
diff --git a/akka-cluster-sharding-typed/src/main/scala/akka/cluster/sharding/typed/javadsl/ShardedDaemonProcess.scala b/akka-cluster-sharding-typed/src/main/scala/akka/cluster/sharding/typed/javadsl/ShardedDaemonProcess.scala
index fbef1bba26..cfead91abf 100644
--- a/akka-cluster-sharding-typed/src/main/scala/akka/cluster/sharding/typed/javadsl/ShardedDaemonProcess.scala
+++ b/akka-cluster-sharding-typed/src/main/scala/akka/cluster/sharding/typed/javadsl/ShardedDaemonProcess.scala
@@ -45,6 +45,20 @@ abstract class ShardedDaemonProcess {
       numberOfInstances: Int,
       behaviorFactory: function.Function[Integer, Behavior[T]]): Unit
 
+  /**
+   * Start a specific number of actors that is then kept alive in the cluster.
+   *
+   * @param behaviorFactory Given a unique id of `0` until `numberOfInstance` create the behavior for that actor.
+   * @param stopMessage sent to the actors when they need to stop because of a rebalance across the nodes of the cluster
+   *                    or cluster shutdown.
+   */
+  def init[T](
+      messageClass: Class[T],
+      name: String,
+      numberOfInstances: Int,
+      behaviorFactory: function.Function[Int, Behavior[T]],
+      stopMessage: T): Unit
+
   /**
    * Start a specific number of actors, each with a unique numeric id in the set, that is then kept alive in the cluster.
    * @param behaviorFactory Given a unique id of `0` until `numberOfInstance` create the behavior for that actor.
diff --git a/akka-cluster-sharding-typed/src/main/scala/akka/cluster/sharding/typed/scaladsl/ShardedDaemonProcess.scala b/akka-cluster-sharding-typed/src/main/scala/akka/cluster/sharding/typed/scaladsl/ShardedDaemonProcess.scala
index 9e655f7c1b..1fde851f2e 100644
--- a/akka-cluster-sharding-typed/src/main/scala/akka/cluster/sharding/typed/scaladsl/ShardedDaemonProcess.scala
+++ b/akka-cluster-sharding-typed/src/main/scala/akka/cluster/sharding/typed/scaladsl/ShardedDaemonProcess.scala
@@ -45,6 +45,16 @@ trait ShardedDaemonProcess extends Extension { javadslSelf: javadsl.ShardedDaemo
   def init[T](name: String, numberOfInstances: Int, behaviorFactory: Int => Behavior[T])(
       implicit classTag: ClassTag[T]): Unit
 
+  /**
+   * Start a specific number of actors that is then kept alive in the cluster.
+   *
+   * @param behaviorFactory Given a unique id of `0` until `numberOfInstance` create the behavior for that actor.
+   * @param stopMessage sent to the actors when they need to stop because of a rebalance across the nodes of the cluster
+   *                    or cluster shutdown.
+   */
+  def init[T](name: String, numberOfInstances: Int, behaviorFactory: Int => Behavior[T], stopMessage: T)(
+      implicit classTag: ClassTag[T]): Unit
+
   /**
    * Start a specific number of actors, each with a unique numeric id in the set, that is then kept alive in the cluster.
    * @param behaviorFactory Given a unique id of `0` until `numberOfInstance` create the behavior for that actor.