A "Rotating Choose Your Own Adventure" game is simple. It's like a regular choose-your-own-adventure game, but instead of me writing out the most popular path split for the whole story, each successive player writes what happens and then provides the next set of path splits for the next player to choose from. Here is an example.
***
It's a cold New York afternoon. You are chasing after a man on a bike. Why?
A) He stole my bike!
B) I want the donuts he has
C) For exercise, the man is my coach
D) I really, really hate bikers