It's possible to capture a boss (eg: Fuuka), bring them to the Summit, and 'cuddle' them into liking you. You can then assign them to a staff position, and from there add them to your party.
This is a terrible idea.
Once in your party, Fuuka will betray you the moment you descend the stairs, having her usual pre-battle chat before attacking you, your party members, and your summons. At that point, so far as I can tell, everyone aggroed by Fuuka becomes hostile to Fuuka's current faction (your party), as does anyone who fights back, instantly turning everyone on your team into an enemy of everyone on your team. Basically, this turns the already dangerous situation of entering a new area full of other enemies into a confusing survivor deathmatch in which people who apparently like you (up to and including your summons) are doing their best to bring you down.
It would have seemed more reasonable to me to have Fuuka unable to be captured, or unable to be convinced to like you, or unable to be promoted to a servant position, or unable to be added to your party, or perhaps even unwilling to betray you once successfully recruited (though any other option would've seemed more likely).
Despite all that, having the pre-battle chat again feels sort of buggy, and turning your party members against each other seems like blatant bug territory.