I'll probably end up doing this idea much better than Chronicle.
Have you ever played Silent Hill or Persona?
Basically, I'm thinking a game where reality is layered, and you can "slip" from one into the next, and your actions in one of the alternate reality realms will have an effect within the primary realm which might not always be possible given the full and unadulterated version of the primary realm.
For example, if a girl is stuck in the mental asylum, she might end up jaunting to a post-apocalyptic realm where all the walls have huge holes and everything is rusted out. From there, she could simply walk through the walls, even though it'd be flatly impossible to walk through the walls of the contemporary cells.
One would figure that this proves the existence of the other worlds, but the girls might just be crazy. The guards and doctors all vehemently deny anything unusual, which either means that the girls are just nuts, they're oblivious to any supernatural activity, or they're in on it.
How the jaunts work would be up to the GM, but either the GM decides when the girls travel to another realm, or one girl can decide and then other girls can follow.
I recommend against having more than one girl in a different place at one time; it would get seriously confusing.