You get one key, and that's supposed to mean one computer. And no, you can't make another order under the student discount, etc.
Sometimes people report that they activate on two machines and don't have activation throw a fit, sometimes they don't. But they're not really getting multiple licenses.
The only way to get three licenses at once for sure is via the family pack, where the individual license pricing works out pretty darn close to the student deal. You might want to see if there are those near to you who'd be able to take advantage of that with you.