Right now the only thing required to use the relay is NIP-42.
It’s possible we could adapt this to work for private groups too but I’d need more details. I haven’t kept up too well with the current proposals. Are the messages in these private groups encrypted? How does moderation/access work?
I put together the inbox.nostr.wine prototype that allows anyone to write events that p-tag a user with an inbox and users with inboxes can only query notes they have authored or been p-tagged in. The main focus there is minimizing metadata leaks.