If you are really serious about keeping your games in good condition then you won't use a dolly on stairs at all. The ones without the stair climbing stuff on them bounce the games all over the place, and the stair climbing ones still give me the heeby geebies.
I always just carry my games up the steps manually, there is little chance of an accident then. (Oh, and before you say "But Paige, my cab has to go into the BASEMENT, or I might MOVE in a year", let me just say that I own like 20 games, and I live on the second floor, and have moved several times in the last few years).
If the game is a bit heavy for two people then pull the monitor out. That will usually lighten up any game enough for two men to carry it with ease. Also, ALWAYS have two people when moving games up and down steps, stair climbing dolly or not.