We do this in both of our groups. The morning session will be trading three months my D&D game, and three months another GMs MM game. The night game alternates between a few months of one DM's D&D and the games of various other people in the group who run shorter, more contained games.
It works very well. Different people get to run their games, it keeps things from getting monotonous, and the long-term DM gets a break between seasons.
Switching every few sessions, though, I wouldn't suggest. Aside from memory issues and continuity issues, I think that flow would be a major problem. Sometimes it's hard to jump right into a character, and if it takes someone a couple of sessions to really get immersed, then suddenly they'll be switching up every time they get comfortable. Also, if a session has to be cancelled for real life, that could mess with stuff, too.
All in all, I'd suggest going monthly, or two months, and switching up that way.