It is my understanding that the SAS engine will only execute the same stored process once at a time. Thus, multiple calls to the same stored process will be batched by the server and executed serially. Is there any way to change this behavior so can have multiple instances of same stored process executing at the same time?
Have you tried it? It would be surprising to me (and disappointing) if what you wrote is true. As long as your stored process server is configured to allow multiple simultaneous sessions, I would expect two users to be able to run the same stored process at the same time.
Perhaps try it with a few friends, and a stored process that sleeps for 10 seconds.