You have a good idea there. Peope who all added to the story would make it like a 'role play' tread. Where each person submitted a character and then had control over the actions of their character only. And then the characters could form poly relationships and write about it from that perspective.
I was originally thinking of a novel-style work that I might write and post for the enjoyment of all.
But I really like this idea of a group effort.