Just as you can send a message when you deny an invite.....
How about when the host of a game, more so when it's an alternate shot game, can send a message to who they are inviting.
Scenario> I start a game of alt shot and already have a Partner I want to play with, then a third player joins and I ask if they have any p that they would like to join them so I invite by player id and they usually turn it down since they do not know me, but if I could say "hey, so and so would like to invite you as a partner" along with the invite, that might be a bit cool.