If one save file is one box, then it works. I've played multiple games with my box at the same time.
I set aside my character decks and go on.
So if I have beaten Skinsaw Murders with Harsk and he has the Deathbane Light Crossbow, that's cool.
But if I want to start another game with Merisiel and go after Burnt Offerings, she's not going to be able to attain the Deathbane Light Crossbow, because it's sitting in the box in Harsk's deck.
Makes sense to me.
Now,if you really wanted to get jiggy, you could allow trading of cards before a scenario between the various characters in that save.