That depends on who determines what message needs to be send out.
Situation Host sends out a message for all:
Host: broadcast message "TheMessage" -> "This is the message." From HostID
Peers: On message received "TheMessage", set Text to Muliplayerobject.Lastmessage
Situation Peer wants a message send to all:
Peer: send message to Host, "NewMessageForAll" from Mulitplayer.MyID
Host: On message received "NewMEssageForAll" -> set Text to Muliplayerobject.Lastmessage and Broadcast message Muliplayerobject.Lastmessage from Multiplayerobject.PeerID (sending peerID here from the message the host gotten from previous peers ID, prevents this message being sent back to the peer where it originated from)
Peers: On message received "TheMessage", set Text to Muliplayerobject.Lastmessage