Another idea: what about a monster whose skills are based on BEING possessed/hacked? So, his attacking skills target his allies, his supportive skills target enemies, etc. That way, when he's possessed/hacked/confused, he's actually a brutal attacker, but until then, he's no good? And maybe has a self-skill to possess himself? That'd be an interesting monster that would completely negate all possession abilities, more interesting than simple immunity, in my opinion.
My idea: self-target skill to possess himself and give himself double damage (Maybe an extra turn instead? Not sure there, extra turns can OP a monster). I'd give this one a single turn cooldown, so you don't use it twice in a row and you quickly have it again if you need to repossess yourself.
Then he has some high damage skills, both AoE and single targets, but they only target allies (meaning you won't use this skill unless the monster is possessed/hacked/confused). They could throw in some negative status effects if some sort if desired. Most possessions last only one turn, so you'd want his damage to be sufficiently high for it be of any real value.
A skill that gives a single enemy immunity to possession (again, you'd only want to use it when possessed). It could be AoE, but then he'd guaranteed have possession immunity and you don't want that. With a single target, it's more likely that you'll give it to a random ally than giving it to himself (although that's still a possibility).
Maybe skills that clear all negative status effects from all enemies and/or clear all good effects from all allies.
His trait obviously couldn't be immune to possession. And you wouldn't want any hardened or tough either, because you'd want the possession to land.
As I said, he'd only be worth anything when possessed. But the interesting part is you'd also have no control which skill got used and what target got hit. So the skills would need to be a bit OP'ed in order to balance the lack of control.