You could use a second datastorage which gets polled for information regularly.
For instance, you use the c2mp to build the rooms, and each player, when in a different room, hosts or is part of that individual room.
Next to that use something like php/mysql or firebase to store extra information relating to your gaming session/profile.
Example: you could store messages in a database, intended for another player. The other player polls the database searching for messages directed at him/her.
To overcome a unique, lasting ID, you could simply create a special ID when a player first connects, based on their IP and Device, and have that ID stored on the users device and in the remote database, and use it to store information or address another player.
Functionally: This ID should be used/transmitted in the c2mp communication by means of text communication when players interact over the c2mp.