I'd go for making a Mistery Dungeon-esque PvE
as in: you send 1 or 2 pokemon of yours to the dungeon, then you control them and the other people do the same, then you go up/down until you reach the boss, then you get into some kind of lobby and form a party that is composed of 1-6 Pokemon in total
as for the movement, it should be mouse based, why? so everyone synchronices and take their turns accordingly (remember, 1 step = 1 turn)