I think a barebones inventory system would really allow for more emphasis on the teamwork and tactical-side of gameplay. What I mean by barebones, is something like maybe in CS:GO, where you can drop your guns and/or grenades so that other players can pick them up. It'd also be cool if you could pick up your dropped mags from the floor, and maybe have a viable way to drop magazines on the floor for friends with the same gun to pick up.
A good example of philosphy of design: Mid game, you feel you have a good angle on a doorway and want to toss in a flash or a grenade, but don't have one. You can ask a friend to quickly drop a grenade near you where you can pick it up without moving from the spot or fumbling with eachother, and then throw it into the doorway.
It's also be nice to help a brother out when he runs out of mags on his mk18 and you have some spare m4 mags.