



 
Steve, Suppose the three teams are players 1, 2, 3, players 4, 5, 6, and players 7, 8, 9. There is a schedule where, over three days, any two players on different teams have played together exactly once:
It is possible to fill in the remaining days to get every pair together at least once. Necessarily some pairs will be together more than once over the 6 days. Here is something that seems pretty good:
Maybe something like this will work for you?  


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