Upvote:3
What you have is already a short-stay Schengen visa so you are in effect asking whether you can extend an existing Schengen visa or apply for another one while you are in the area and the answer is generally no.
The rules for national visas are different and there are situation in which it could in theory be possible to apply for a long-stay study visa. While it's difficult to know exactly without much more details, that is probably impossible in your situation.