We could, perhaps, create a list of the supplies we go through the most, and then decide who can provide what?
Health Pots: Nobody really used these, as people were always really prompt about healing teammates
Bandages: Definitely need these.
Feathers: These run out fast too.
Spare Weapons?: I have a black flamemare filled with a pretty large variety of, albeit semi-weak, weapons. (Daggers, bastard swords, instruments, crossbow, knuckles, a staff that I swear to god if anyone steals I'm cutting off your nipples)
Mana Pots: I usually just switch to melee when I'm out of mana, so I've never had a huge problem in this department, not sure how it is for more dedicated mages.
Stamina Pots: We have this thing called... Enduring Melody. Unless you're Bar, then you don't even use stamina pots so I don't think we really need these.
Alternatively, looking at the things we actually need, It wouldn't be very hard for everyone to provide their own supplies. I think the only reason that THE DUNGEON NOT TO BE NAMED was so tricky is because none of us bothered to do any large scale stocking up. And ghost/ghasts, but still, everyone ran out of feathers on like, floor 3,