While you may think that you only need two moves depending on the size of your home, a third move is likely to speed up the process. People who move get tired and start working more slowly as they wear out. Specifically, two carriers can transport your heavy furniture, while another carrier packs your belongings in boxes and transports them. The important thing is to ask if there will be lost time with 3 moving agents (if one of the movers will be inactive for part of the time).
There are several different reasons for this. Sometimes, a larger company will try to keep more movers working during slow periods so they don't have to re-hire when business picks up. Sometimes a company that operates, say, 3 trucks and crews, but legitimately does a lot of moving larger houses, so they need that third carrier on each team.