Might depend on the chain and/or the property, but I've never had a problem with multiple consecutive reservations at different rates. I've never even had to vacate the room - just told the front desk I had another reservation, settled up the paperwork, and stayed right thru.

BTW, if you're deeing these rates online, it might be worth a phone call. A human agent may be able to combine the separate rates into a single reservation with a rate change, saving you the hassle & the worry.