Trying to extend the Scheduler interface according to the comments at

rxjava-core/src/main/java/rx/Scheduler.java

@@ -19,12 +19,31 @@
 
 import rx.util.functions.Action0;
 import rx.util.functions.Func0;
+import rx.util.functions.Func1;
+import rx.util.functions.Func2;
 
 /**
  * Represents an object that schedules units of work.
  */
 public interface Scheduler {
 
+    /**
+     * Schedules a cancelable action to be executed.
+     * 
+     * @param state State to pass into the action.
+     * @param action Action to schedule.
+     * @return a subscription to be able to unsubscribe from action.
+     */
+    <T> Subscription schedule(T state, Func2<Scheduler, T, Subscription> action);
+
+    /**
+     * Schedules a cancelable action to be executed.
+     * 
+     * @param action Action to schedule.
+     * @return a subscription to be able to unsubscribe from action.
+     */
+    Subscription schedule(Func1<Scheduler, Subscription> action);
+
     /**
      * Schedules a cancelable action to be executed.
      * 
@@ -43,6 +62,27 @@ public interface Scheduler {
      */
     Subscription schedule(Action0 action);
 
+    /**
+     * Schedules a cancelable action to be executed in dueTime.
+     * 
+     * @param state State to pass into the action.
+     * @param action Action to schedule.
+     * @param dueTime Time the action is due for executing.
+     * @param unit Time unit of the due time.
+     * @return a subscription to be able to unsubscribe from action.
+     */
+    <T> Subscription schedule(T state, Func2<Scheduler, T, Subscription> action, long dueTime, TimeUnit unit);
+
+    /**
+     * Schedules a cancelable action to be executed in dueTime.
+     * 
+     * @param action Action to schedule.
+     * @param dueTime Time the action is due for executing.
+     * @param unit Time unit of the due time.
+     * @return a subscription to be able to unsubscribe from action.
+     */
+    Subscription schedule(Func1<Scheduler, Subscription> action, long dueTime, TimeUnit unit);
+
     /**
      * Schedules an action to be executed in dueTime.
      * 

rxjava-core/src/main/java/rx/concurrency/AbstractScheduler.java

@@ -22,6 +22,8 @@
 import rx.subscriptions.Subscriptions;
 import rx.util.functions.Action0;
 import rx.util.functions.Func0;
+import rx.util.functions.Func1;
+import rx.util.functions.Func2;
 
 /* package */abstract class AbstractScheduler implements Scheduler {
 
@@ -30,11 +32,51 @@ public Subscription schedule(Action0 action) {
         return schedule(asFunc0(action));
     }
 
+    @Override
+    public Subscription schedule(final Func1<Scheduler, Subscription> action) {
+        return schedule(new Func0<Subscription>() {
+            @Override
+            public Subscription call() {
+                return action.call(AbstractScheduler.this);
+            }
+        });
+    }
+
+    @Override
+    public <T> Subscription schedule(final T state, final Func2<Scheduler, T, Subscription> action) {
+      return schedule(new Func0<Subscription>() {
+          @Override
+          public Subscription call() {
+              return action.call(AbstractScheduler.this, state);
+          }
+      });
+    }
+
     @Override
     public Subscription schedule(Action0 action, long dueTime, TimeUnit unit) {
         return schedule(asFunc0(action), dueTime, unit);
     }
 
+    @Override
+    public Subscription schedule(final Func1<Scheduler, Subscription> action, long dueTime, TimeUnit unit) {
+      return schedule(new Func0<Subscription>() {
+          @Override
+          public Subscription call() {
+              return action.call(AbstractScheduler.this);
+          }
+    }, dueTime, unit);
+    }
+
+    @Override
+    public <T> Subscription schedule(final T state, final Func2<Scheduler, T, Subscription> action, long dueTime, TimeUnit unit) {
+        return schedule(new Func0<Subscription>() {
+            @Override
+            public Subscription call() {
+                return action.call(AbstractScheduler.this, state);
+            }
+        }, dueTime, unit);
+    }
+
     @Override
     public long now() {
         return System.nanoTime();

rxjava-core/src/main/java/rx/operators/Tester.java

@@ -19,6 +19,7 @@
 import rx.util.functions.Action0;
 import rx.util.functions.Func0;
 import rx.util.functions.Func1;
+import rx.util.functions.Func2;
 
 /**
  * Common utility functions for testing operator implementations.
@@ -289,6 +290,16 @@ public Subscription schedule(Func0<Subscription> action) {
                 return underlying.schedule(action);
             }
 
+            @Override
+            public Subscription schedule(Func1<Scheduler, Subscription> action) {
+                return underlying.schedule(action);
+            }
+
+            @Override
+            public <T> Subscription schedule(T state, Func2<Scheduler, T, Subscription> action) {
+                return underlying.schedule(state, action);
+            }
+
             @Override
             public Subscription schedule(Action0 action, long dueTime, TimeUnit unit) {
                 return underlying.schedule(action, dueTime, unit);
@@ -299,6 +310,16 @@ public Subscription schedule(Func0<Subscription> action, long dueTime, TimeUnit
                 return underlying.schedule(action, dueTime, unit);
             }
 
+            @Override
+            public Subscription schedule(Func1<Scheduler, Subscription> action, long dueTime, TimeUnit unit) {
+                return underlying.schedule(action, dueTime, unit);
+            }
+
+            @Override
+            public <T> Subscription schedule(T state, Func2<Scheduler, T, Subscription> action, long dueTime, TimeUnit unit) {
+                return underlying.schedule(state, action, dueTime, unit);
+            }
+
             @Override
             public long now() {
                 return underlying.now();