Yes this is possible. For example:
(1 8 5 9) ( 3 11 10 7) (4 12 6 2)
(7 6 5 4) (12 2 11 1) (3 10 9 8)
(9 11 5 6) (12 8 4 10) (2 7 1 3)
(4 7 8 11) ( 9 6 12 3) (1 2 10 5)
(2 4 3 9) ( 1 6 11 8) (5 10 12 7)
(8 2 10 6) ( 5 12 3 11) (7 9 1 4)
Of the 66 possible pairs, 28 occur together once, 34 occur together twice and 4 occur together three times. The latter are (1 2), (4 7), (3 9) and (8 10)
