The simple solution to a big server would be to add two tag team spar rooms. There would be a lobby and a waiting room for each room. Inside the lobby you can click on a friends/randoms profile and "request to be partner." Once you have a partner, you can enter the waiting/spar room, and que. If and only if both partners are qued, you get added to the que. One room can be a regular TT spar room, the second can be a TT spar streak room.
Could also be a TT spar score underneath the 1vs1 spars, that show overall seasonal score. This way there can be a TT spar tournament with the best rated Tag Team sparrers.