There’s been attempts at this in the past. I think the last one’s still being worked on.
So you can probably get some tips from the participants there. I’m sure it’ll be a lot of fun for people.
I wouldn’t do
Instead I’d suggest using the vignette structure of Choice of Games to your full benefit. Create a central theme, then let everyone write individual vignettes that aren’t connected to each other. You can stitch them together later. Or you can let each vignette writer pick some important information that they’re going to have carry over.
It means everyone can work on their vignettes at the same time. And that you’re not reliant on any single writer failing to deliver their piece on time, and thus delaying the whole project. It also gives people freedom to make their sections as long or as short as they like.
I’d take a leaf out of the books of tv shows that have self-contained episodes. So if your game’s about a Captain that flies around the galaxy on their starship, visiting strange new worlds, seeking out new life. Well every player can write their own alien encounters, or visit to new planets, or other exciting adventures. You can even make it so the player can choose which order they do things in.
With the likes of a Captain on a starship, they fly off at the end of the episode, everyone’s learned a lesson, but they rarely refer to what happened in previous episodes. They generally end in a sort of soft-reset.