"Loss" of Loot between the Bosses in the Boss-Rush

Unfortunately, I had to end the Boss Rush after my 5th run because my inventory was already full, and I didn’t want to "delete" any loot from the Chests between each Bosses.

My companion's inventory is also full, as I moved over everything I could after the 3rd run.

Would it be possible to introduce a kind of "extra inventory" where you can collect all of your loot at the end of the last run in the Boss Rush?

This way, the loot chest could be removed, and at the end, you would receive all the loot from all runs together, perhaps in the rewards tab or something similar.