About the best you can do is the following:
(6 9 v 5 10) (12 8 v 1 7) (11 4 v 2 3)
(4 7 v 6 11) (10 9 v 2 8) (12 5 v 3 1)
(5 8 v 4 12) (11 7 v 3 9) (10 6 v 1 2)
(2 11 v 1 5) ( 8 9 v 3 6) (10 4 v 7 12)
(3 12 v 2 6) ( 9 7 v 1 4) (11 5 v 8 10)
(1 10 v 3 4) ( 7 8 v 2 5) (12 6 v 9 11)
where all the partnerships are different and all pairs oppose at least once.
Hope that helps.
