BigGrecian.
I believe that if you are sponsored by School A, leave and then wish to return to School B, that you need to get the Visa transferred (assuming that it is still in currency) to the new School and if you were in good standing with the previous School A..
I do not believe that you can just walk into School B - as they are not your sponsor according to the Visa in the passport.
The Sponsor is basically responsible for your time in the US.
That was the point I was making.