Hear me out here. Your friends you bring along don't really need to be part of the story's cutscenes and all that, everyone will still watch their own cutscenes on their own consoles or PCs. What will happen is that you and your friend(s) will do the playable part of the game's story together and since this is invite only, there should be no worries about waiting for friend to get ready, even if your friend has a bad connection, it shouldn't be the same as waiting for a 12th person to show up in a MPA of a challenge room. What should happen while you were waiting is that you'll spawn in with no enemies first until your friend also spawns in with you and then you'll fight the (buffed) boss or enemies together. Afterwards the cutscenes will treat what you've done as if you did it anyway.
I think that's the simplest way I can explain it without making it too complicated to implement, it could even be part an update that will be implemented along with this game's future episodes.