LOTRO has a nice feature for this, a "Pending Loot" bag which is just inventory overflow space where any excess items you get as loot drops can land. You've then got an hour in which to take them out. (When that hour expires they disappear if you haven't removed them by then.) That gives enough time to finish a run, get back to town, and sort out your stuff to make space for the new drops.
I wish they'd put something like that in this game.
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