This is the basis of what "role-playing" is-or, at least, the type of role-playing that I have participated in online. It's all about collaboratively writing stories by doing a paragraph or two-however much is deemed necessary to keep the prompt alive between you and your partner. A turn-based method of writing, and one of the rarer and lesser-known ones. Together, you work on the idea, the characters, the setting, and the plot. You may even come up with more as you continue through your process of writing together.