Create community specific moderators.
I mod for team Tempo Storm. Every streamer is added to the Tempo Storm community which we use to promote who is online in our website or through apps or bots on discord/curse. My role is to ensure every team member, no matter which game they are playing, is doing well and chat is behaving. This is sometimes hard to do if the streamer hasn't met me through the team contacts, or some other reason. These streamers may be hesitant to mod me or others like me in the same role.
So my suggestion is to add a community based global moderator for team managers and staff to be instantly recognized and trusted when entering a streamers channel that belongs to your team.
Twitch name: Hazard_TS
Tempo Storm: Assistant Community Manager

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TheBoland commented
Only the broadcaster should be allowed to add/remove channel moderators.
If this gets added as a feature then a simple option needs to be added for the broadcaster to allow moderators from certain teams/communities which should be off by default.