Is the schedule below useful? The cyclic pattern where one round can be generated from the previous one, means that everyone will play exactly 4 times on each field. But is 24 rounds too many?
Field 1 Field 2 Field 3 Field 4 Field 5 Byes
(24 16 v 23 6) ( 4 17 v 19 21) (14 5 v 9 8) (10 13 v 11 1) (12 7 v 20 2) (15 18 3 22)
( 1 17 v 24 7) ( 5 18 v 20 22) (15 6 v 10 9) (11 14 v 12 2) (13 8 v 21 3) (16 19 4 23)
( 2 18 v 1 8) ( 6 19 v 21 23) (16 7 v 11 10) (12 15 v 13 3) (14 9 v 22 4) (17 20 5 24)
( 3 19 v 2 9) ( 7 20 v 22 24) (17 8 v 12 11) (13 16 v 14 4) (15 10 v 23 5) (18 21 6 1)
( 4 20 v 3 10) ( 8 21 v 23 1) (18 9 v 13 12) (14 17 v 15 5) (16 11 v 24 6) (19 22 7 2)
( 5 21 v 4 11) ( 9 22 v 24 2) (19 10 v 14 13) (15 18 v 16 6) (17 12 v 1 7) (20 23 8 3)
( 6 22 v 5 12) (10 23 v 1 3) (20 11 v 15 14) (16 19 v 17 7) (18 13 v 2 8) (21 24 9 4)
( 7 23 v 6 13) (11 24 v 2 4) (21 12 v 16 15) (17 20 v 18 8) (19 14 v 3 9) (22 1 10 5)
( 8 24 v 7 14) (12 1 v 3 5) (22 13 v 17 16) (18 21 v 19 9) (20 15 v 4 10) (23 2 11 6)
( 9 1 v 8 15) (13 2 v 4 6) (23 14 v 18 17) (19 22 v 20 10) (21 16 v 5 11) (24 3 12 7)
(10 2 v 9 16) (14 3 v 5 7) (24 15 v 19 18) (20 23 v 21 11) (22 17 v 6 12) ( 1 4 13 8)
(11 3 v 10 17) (15 4 v 6 8) ( 1 16 v 20 19) (21 24 v 22 12) (23 18 v 7 13) ( 2 5 14 9)
(12 4 v 11 18) (16 5 v 7 9) ( 2 17 v 21 20) (22 1 v 23 13) (24 19 v 8 14) ( 3 6 15 10)
(13 5 v 12 19) (17 6 v 8 10) ( 3 18 v 22 21) (23 2 v 24 14) ( 1 20 v 9 15) ( 4 7 16 11)
(14 6 v 13 20) (18 7 v 9 11) ( 4 19 v 23 22) (24 3 v 1 15) ( 2 21 v 10 16) ( 5 8 17 12)
(15 7 v 14 21) (19 8 v 10 12) ( 5 20 v 24 23) ( 1 4 v 2 16) ( 3 22 v 11 17) ( 6 9 18 13)
(16 8 v 15 22) (20 9 v 11 13) ( 6 21 v 1 24) ( 2 5 v 3 17) ( 4 23 v 12 18) ( 7 10 19 14)
(17 9 v 16 23) (21 10 v 12 14) ( 7 22 v 2 1) ( 3 6 v 4 18) ( 5 24 v 13 19) ( 8 11 20 15)
(18 10 v 17 24) (22 11 v 13 15) ( 8 23 v 3 2) ( 4 7 v 5 19) ( 6 1 v 14 20) ( 9 12 21 16)
(19 11 v 18 1) (23 12 v 14 16) ( 9 24 v 4 3) ( 5 8 v 6 20) ( 7 2 v 15 21) (10 13 22 17)
(20 12 v 19 2) (24 13 v 15 17) (10 1 v 5 4) ( 6 9 v 7 21) ( 8 3 v 16 22) (11 14 23 18)
(21 13 v 20 3) ( 1 14 v 16 18) (11 2 v 6 5) ( 7 10 v 8 22) ( 9 4 v 17 23) (12 15 24 19)
(22 14 v 21 4) ( 2 15 v 17 19) (12 3 v 7 6) ( 8 11 v 9 23) (10 5 v 18 24) (13 16 1 20)
(23 15 v 22 5) ( 3 16 v 18 20) (13 4 v 8 7) ( 9 12 v 10 24) (11 6 v 19 1) (14 17 2 21)
Each player above will have 20 different partners and will see all other players in opposition either once or twice.
12 rounds is a much harder problem, but I think I have found something that will work.
Field 1 Field 2 Field 3 Field 4 Field 5 Byes
( 3 15 v 20 16) ( 6 19 v 1 7) ( 5 4 v 10 14) (23 2 v 13 22) (17 9 v 24 8) (18 12 21 11)
( 4 16 v 21 17) ( 1 20 v 2 8) ( 6 5 v 11 15) (24 3 v 14 23) (18 10 v 19 9) (13 7 22 12)
( 5 17 v 22 18) ( 2 21 v 3 9) ( 1 6 v 12 16) (19 4 v 15 24) (13 11 v 20 10) (14 8 23 7)
( 6 18 v 23 13) ( 3 22 v 4 10) ( 2 1 v 7 17) (20 5 v 16 19) (14 12 v 21 11) (15 9 24 8)
( 1 13 v 24 14) ( 4 23 v 5 11) ( 3 2 v 8 18) (21 6 v 17 20) (15 7 v 22 12) (16 10 19 9)
( 2 14 v 19 15) ( 5 24 v 6 12) ( 4 3 v 9 13) (22 1 v 18 21) (16 8 v 23 7) (17 11 20 10)
( 9 4 v 7 19) (20 13 v 17 12) (11 24 v 16 22) ( 6 14 v 8 10) ( 3 21 v 5 15) ( 1 18 2 23)
(10 5 v 8 20) (21 14 v 18 7) (12 19 v 17 23) ( 1 15 v 9 11) ( 4 22 v 6 16) ( 2 13 3 24)
(11 6 v 9 21) (22 15 v 13 8) ( 7 20 v 18 24) ( 2 16 v 10 12) ( 5 23 v 1 17) ( 3 14 4 19)
(12 1 v 10 22) (23 16 v 14 9) ( 8 21 v 13 19) ( 3 17 v 11 7) ( 6 24 v 2 18) ( 4 15 5 20)
( 7 2 v 11 23) (24 17 v 15 10) ( 9 22 v 14 20) ( 4 18 v 12 8) ( 1 19 v 3 13) ( 5 16 6 21)
( 8 3 v 12 24) (19 18 v 16 11) (10 23 v 15 21) ( 5 13 v 7 9) ( 2 20 v 4 14) ( 6 17 1 22)
Above everyone gets 2 byes, plays twice on each field, has 10 different partners and 20 different opponents. There are 12 pairs of players who never meet either as partners or opponents, these are:
( 1 4)
( 2 5)
( 3 6)
( 7 10)
( 8 11)
( 9 12)
(13 16)
(14 17)
(15 18)
(19 22)
(20 23)
(21 24)
Finally there are some players who have 2 consecutive byes in rounds 7 to 12, but I think this could be avoided if you rearrange the order of the rounds.
Can you tell us what a game of Caps involves? I have no idea myself.