Do I need to purchase a new re-entry permit after changing schools on a non-B visa extension?

if you had a yearly extension and a multiple re-entry permit it was issued because you were employed by a specific employer, and when you left them, you had to cancel that extension and apply for a new extension using documents from the new employer..

I would say the multi-re-entry permit from the old extension is not good because the extension you got it on was cancelled

Go ask the immigration office where you got this new extension and see what they say but as I said I think that one is no good and you need to get a new one that's tied to this current extension

What do you mean by "transfer visa with my new school"?