A-ha! You didn't say that in your OP brother.
I've found no way to add peeps to an existing chat. Experienced this recently. Turned out I had to create a new chat in order to include the desired members.
IIRC Brian might've been in that one so he'll prolly remember.
Hang on... here's my final reply in that conversation:
Maybe you have to be the Conversation starter?
Brian found an option (he was the starter and I requested he add you), but it didn't work. I assume he's gonna try again.
Otherwise... hang on... I could try starting a dummy convo and if I'm able to add both of you, I'll copy Brian and my posts over to it.
Here goes...
It worked! Obviously you have to be the starter. Don't think it was always this way; could be a setting on the back end.
You'll receive the new Conversation shortly...
So it would seem that you have to be the starter. If you were the starter, my secondary theory that it can only be done upon-creation comes into-play.