With 7 players, you could play this:
[(D G):(B E)]
[(B F):(A G)]
[(C G):(A E)]
[(B D):(C F)]
[(A F):(C E)]
[(B C):(D E)]
[(D F):(E G)]
[(A C):(B G)]
[(A B):(E F)]
[(F G):(C D)]
However the pair of players AD neither partners nor opposes, and have one less game than the others.
