Okay, so instead of having a formal trading system that would break the game. Why not only be able to trade items that you just acquired from a raid/etc with your fire team? Ofc have a time limit as to when you can trade. Say you have two hunters in your fire team and you do the raid? One gets the boots but he already has the boots. And the other hunter gets the helmet but he already has the helmet. They could trade their prizes within, say a 30 minute time frame.
Just an idea.