I'm so conflicted on this idea. On one end of the rainbow there's google docs which would allow you to do all of this among a bunch of people you already know perfectly well, as long as people agree to follow the rules.

on the other end there's a great way to make this like a brilliant game of sorts- 4 random people get put into a chat room of sorts, the room has a theme/prompt and turn by turn they get to respond to the chat with fiction. idk who wins but at the end of the game you can publish the entire chat as a story.