Game idea? Player characters are pulled into the BTR - the Bureau of Temporal Regulations and asked to help set the timeline straight. Players would go into different people's worlds to finds things that are making the time stream wonky and fix it.

Though they'd have to follow Strict Rules because the BTR is all about paperwork and proper management. That, however, doesn't mean that the players will actually do that.

They can go and make their own temporal messes. Or try to fix the timelines how they wanted them to be fixed.

Of course people's worlds would be affected. (After all they're in the BTR and not at home which causes problems...)