In multi-streams each party merges its ban list for the multi-stream session. So if streamer A bans you and is then doing a multi-stream with streamer B, you can not use the chat in the multi-stream.
Sometimes streamer A and B forget to leave the multi-stream session for days. So even if streamer A is offline, you can still not use the chat in streamer B's channel. You have to remind streamer B to leave the session in order to split the ban list again.
We won't change this system in the near future, so please avoid being banned or remind the specific streamer.
If you were band during a multi-stream session, your ban counts for the streamer or his moderator who banned you. So if streamer A banned you during multi-stream and leaves the session, you can not use streamer A's chat afterwards, but you can use streamer B's chat now.