It's possible but it will be a pain. I just booked my 2 night stay for Feb and was told that between the 1st and 2nd night I will need to stop at registration to re-reg, and that is all on my card.
We did that between my wife and I and they make you check out and check back in (you keep the same room) it took 5 minutes each morning at the front desk it was pretty painless.
I just booked two consecutive nights at the luxor and they linked them without my having to check out and back in again. The lady I spoke with just made notes on my reservation when I booked.