I think 3 isn't enough. Or even so you can run up to 6 during nightfalls or strikes adding further difficulty for yet another way to get better gear. And have a set for the raids and nightfall to have matchmaking because not everyone can find people to raid with all the time. It's really annoying to try and do a raid and people quit out and you have to wait forever to find another to join. At least at some point let it matchmake people into it.
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At least 6 just like the raid.