Q for RW AIRLINE Pilots Please

A quick question for those of you who fly for real air carriers. Are all pilots assigned to a single aircraft type at any given time (regardless of the number of actual type ratings they may have), or do some fly more than one type over a rotation or on subsequent rotations? For example, if a pilot (Captain or FO) is type rated for a 737-200 and a 727 for example, would he only be assigned to one or the other, or might he get to fly both in a given period of time (say a couple to 4 months)?Many thanks!Glenn