There are no overflow items to swap between the characters. When either of the View All buttons is pressed it shows all the cards for the entire party and even there Weapons will show, for example, 13/14.
In my last game Harsk was constantly banishing a card each time the site needed a temporary close when another party member was facing the final boss. I won the scenario, but now Harsk has too few cards and no other party member has the extras to fill those slots, nor are there any left over surplus items that can fill the slots he needs to fill.
This has happened with various characters, not just Harsk, and not just in that one scenario.
NB: I am playing solo storymode.