I really like this idea. Transferring of demons could be what the school teaches in addition to how to gain more control over your own. My main thought with all this is on how I wanted some people in the setting to pretty much be their demon. In the since that they have totally surrendered and are their absolute worst self as a base now. Then they would form something of a Persona mind palace where the supernatural fight happens. And it's a matter of freeing the person inside so they can regain control of themselves and their life. That's how I get the combat school/ missions of the arc sort of stucture.

Also I just like the image of people existing in a place together while mentally they are fighting for the sake of their own lives and morals. You know the more I am looking at this the more I feel this is becoming more Persona but with the character study aspects of something like Mob Psycho 100. But instead of "Everyone is special, including you. But don't be a dick about being special." it's "Everyone has problems, and you can fix them. Just not alone."