I've no idea how this would work, but I just had this concept in mind (plus is would be trippy as heck!):

Instead of through introspection and monologue, the idea would be to portray what make each character themselves would be through words and action seen through the eyes of the poor mooks/baddies/rivals they would face. That would be a huge study in characterization and perspective, in that each player would effectively try to impact each scene as much as they can through actions and words alone. The plot would probably be pretty big on action, and the pace would probably means shorter but faster posts as a result.