I tend to play the same person for a few games in a row and think you should be able to click a rematch button from within the hangout to start another game. 

I realise this could cause problems with streamed games but surely this could be implemented on standard hangouts rather than on air ones.

I just find it a pain when you are chatting to someone to need to shut the hangout to reload another.

Any thoughts.

Great suggestion, I'm sure it'd be a simple addition to the functionality that's already there, it's only a matter of time before it's an option eh!