I have had the same situation when I wanted to extend a two night stay to a three night one. I had two options:
1) Book the third night as a one-nighter at the new higher rate, but keep the original two nights at the lower rate, or
2) Speak to "in-house" reservations and see if he/she could extend the stay at the same rate.

The strategy is to go for (2) first. This I did and it suceeded. If it had not suceeded I would have bought the third night at the prevailing rate without touching the first two nights.

It is very very very very unlikely that you will be asked to move, (unless you bought a suite on the first night and paid for a bit of concrete in the parking lot on the second night).

Why they do not move is its a hassle for the guests which they really do want to avoid if its not necessaery, and its a hassle and cost to the hotel (Beds definetly need new sheets, towels, soaps etc etc etc - Belboy has to move luggage [and u dont have to tip])

So do not worry too much.