Crazy idea: a sandbox game with no regular group, in the style of the West Marches but with the setting that powers it shared between multiple DMs.
This could just be on the design end: you have multiple people collaborating on a setting that one of them then uses to run a game. Co-operative worldbuiling. Or you could get fancier, and have each participating DM run their own player pool through the game.
Which could, in turn, run a couple of ways. You could have multiple independent games, seperated geographically or by convention, or you could have multiple DMs supporting the same player pool, with players switching back and forth between games. My personal situation better supports the former option, since I don't know many other DMs locally. But the second option could be interesting.
There big issues I've identified so far are time-keeping, DMing style, and griefing.
That last is also the least important; though I assume there's some potential for one DM to put way to powerful monsters in places they're not supposed to be, without warning for the players or the other DMs, a little thought put into who you invite into the project ought to keep the chance to a minimum. A bigger problem would be people doing that kind of thing accidentally, but that would happen even in a single-DM game.
Slightly bigger issue is time-keeping; if you put everyone on personal time, affected solely by in-game activities, as I tend to do in my normal games, then you could potentially end up with some groups way behind others, depending on how active the different DMs are. Then you get weirdness like dungeons that haven't been cleared out yet, but will be, so you can't go there because of what will happen, but hasn't. My solution would be to put everyone on universal time, perhaps locked to real-world time, and your character hangs around in taverns until you take them out on another adventure. (Which seems like a perfectly reasonable thing for a character to do.)
Finally, DM style. Part of the idea behind the set-up would be to produce an environment with greater depth and variety than one DM can provide, but this could go too far. And everyone involved would have to use a similar format in their world notes, and a similar level of rigor in applying those notes.
This could work, and it might be fun. It's not something that's likely to happen; I'm probably too distractible to pull something like that off. The vision I have in my head is of a game that keeps going for years, with different players and different DMs, but one persistent world. But at least in my case, it's more likely to stay just as an idea.
EDIT: Reposted because I just realized I misspelled the title. Why do I keep doing that?