I know someone who did this, though it was within the same university and she already had a faculty member willing to take her on. She avoided having to apply to a new program, which I think is the biggest hurdle.
I know people who have changed programs (Ph.D--> Ph.D, Psy.D--> Psy.D., etc), and they had to re-apply completely, and then transfer credits, which seemed like a big PITA.