Coincidentally, I was just told today by an online chat with a CM that he believes I could book up to three rooms. Which makes sense, as with a PIN I was able to do that too. I didn't end up calling as my SIL got a different discount so I can't confirm for sure!
Update 6pm: my SIL other discount fell through (she waited too long to book). We called Disney and they were able to book her a room (in her own name) using my AP discount. They said the AP holder has to be at check in with them, which is no problem, since we're traveling together. So from my experience tonight, the answer is YES, you can
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