That would make sense but then you basically have 2 party, with one that only matters in fights... (I guess it could run on the same engine as my proposed Digimon game

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But I think that having a shared monster for the party would make it easier to have two different action going on at the same time, with the humans up to something while the monsters battle. I would also assume the Monster fight would be simpler affairs where you're trying to stun the opponent so you can lan your devastating finisher.