> this is pretty much what Matrix does, if I understand correctly.
I think it has senders encrypt messages with each room member's public key, rather than a single shared key. (At least, that's what the behavior I've seen suggests to me.)
Here's the spec, in case you want to comb through it:
> When creating a Megolm session in a room, clients must share the corresponding session key using Olm with the intended recipients, so that they can decrypt future messages encrypted using this session. An m.room_key event is used to do this. Clients must also handle m.room_key events sent by other devices in order to decrypt their messages.
Additionally the key is regularly updated to provide some degree of perfect forward secrecy and avoid encrypting for people who left the group chat