From the options that you give I can only make things work if you have 20 players and 5 rounds with each player having one break each. In the schedule below each player's 4 partners and 8 opponents and all different.
Table 1 Table 2 Table 3 Table 4 Break
(10 20 v 11 19) (16 15 v 3 14) (1 6 v 5 17) ( 7 12 v 8 4) (2 9 18 13)
( 6 16 v 12 20) (17 11 v 4 15) (2 7 v 1 18) ( 8 13 v 9 5) (3 10 19 14)
( 7 17 v 13 16) (18 12 v 5 11) (3 8 v 2 19) ( 9 14 v 10 1) (4 6 20 15)
( 8 18 v 14 17) (19 13 v 1 12) (4 9 v 3 20) (10 15 v 6 2) (5 7 16 11)
( 9 19 v 15 18) (20 14 v 2 13) (5 10 v 4 16) ( 6 11 v 7 3) (1 8 17 12)
Have a good party.
Ian.