It’s not uncommon for people to chat online with multiple people simultaneously and keep it all straight. Sometimes I really wish you could open up multiple chat windows with the same person so we can talk about different topics simultaneously. I don’t think it’d be any more complicated to keep straight than chatting with multiple people.
I do think two (or more) chat windows with the same person would come in really useful pretty often. But you can’t do it. I tried. Maybe someday Google will realize how limiting it is to only have one conversation with a person at a time.