I am creating a campaign when the PCs would be agents for The Truth Initiative. They are an organization dedicated to keeping reality from collpasing.

There are people in the world who have the ability to edit reality for their own benefit. this has nasty side effects though. It can cause tears in the fabric of reality allowing things from other universes into our own. Most of these things are not good for humans. It can also cause reality inclusions which is where reality folds in upon inself, creating a pocket universe. You can get in but not out. At least without undoing the edit. The bigger the edit, the bigger the side effects.

The players will be survivors of various reality inclusions. They will have the ability to edit reality so they can fix what is broken. They will also have minor super abilities . The history they remember will not always match what the other players remember.

What will be a good system for this?