tTc Nauts APL team

So I'd love to start a small nauts tournament after finals. But We need a few more people to make it more interesting. I'm trying to think of a way to make it so we can shuffle 6 players around, to make multiple teams, example:

1+2+3=Team1 4+5+6= Team 2 and then do a shuffle *randomly*, so 1+5+3=Team 3 and then 2+4+6=Team four and rotate these around so we can all find teams we sort of like.