Gene,
How about twelve rounds of play, where each player gets three breaks during the course of the evening? Below this is arranged in 3 blocks of 4 rounds with all players receiving one break per block.
Table 1 Table 2 Table 3 Break
(L I v D A) (P K v M F) (B O v H G) (J C E N)
(I J v A B) (M L v N G) (C P v E H) (K D F O)
(J K v B C) (N I v O H) (D M v F E) (L A G P)
(K L v C D) (O J v P E) (A N v G F) (I B H M)
(M P v B I) (H A v E C) (O L v F J) (K N D G)
(N M v C J) (E B v F D) (P I v G K) (L O A H)
(O N v D K) (F C v G A) (M J v H L) (I P B E)
(P O v A L) (G D v H B) (N K v E I) (J M C F)
(B N v L E) (F K v H J) (C M v D O) (I G P A)
(C O v I F) (G L v E K) (D N v A P) (J H M B)
(D P v J G) (H I v F L) (A O v B M) (K E N C)
(A M v K H) (E J v G I) (B P v C N) (L F O D)
Each player has 9 different partners, and will oppose all other players at least once, and at most twice.
Hope that helps.
Ian.