Actually this was never a problem with my gaming group WAY back in high school. We were always buying new game systems. We had a nice system worked out where one person would run a campaign for a few weeks, giving the rest of us time to write up notes and study a new game, so that we would be ready to run a campaign of our own when our turn came around. That would give each player a couple months of prep time to run a campaign.
We ended up playing TMNT, Paranoia, Psi-World, Chill, Call of Cthulhu, Stormbringer, D&D, Twilight 2000, Gamma World, Villains and Vigilantes, among others. We would usually come back to CoC or Stormbringer. And if we didn't have anything ready, then we would roll up Traveller characters, start a grand adventure that usually began in a bar, start a bar fight... and then by that time we'd be tired and call it a night. In all the many, many times I played Traveller, I don't think I ever made it past the bar fight, we would have lost our character sheets by the time we played next and we'd start all over.
I think changing up systems is great. It helps you role-play out situations rather than trying to exploit holes in the rules. And it can give you new insights on how to approach situations differently. A tactic you learn using one system might be applicable in another.
So that might be a decent system to try out with your gaming group. The GM can declare that he is going to take a break from the campaign in X weeks, and someone else can run a different setting in the interim and give the regular GM time to recharge his batteries.