Collaborative fiction is its name. I like the idea of passing the story on and seeing where it goes. Usually collabs are partnerships but a collaborative author may focus on a specific protagonist or character in the narrative thread, and then pass the story to another writer for further additions or a change in focus to a different protagonist.

Collaborative fiction - Wikipedia

Link: https://en.wikipedia.org/wiki/Co

This article is about collaborative writing of fiction. For collaborative writing in a technical or academic sense, see collaborative editing.