With 10 players and fivesomes I don't believe you can avoid having some pairs of players play together 4 times. In the schedule below pairs of players occur together either 2 or 4 times.
(3 4 7 10 6) (2 9 1 8 5)
(3 7 1 9 8) (2 6 4 5 10)
(3 5 8 6 2) (10 4 9 7 1)
(3 1 10 6 8) (7 2 9 4 5)
(4 3 8 5 7) (1 10 9 6 2)
(7 3 2 9 6) (10 8 1 5 4)
The 11 player scenario is nicer. It is possible to have pairs together either once or twice, however the distribution of players is not even across the foursomes and threesomes. For example player 1 is never in a threesome.
( 2 6 1 5) ( 4 3 10 11) (9 7 8)
( 7 4 9 5) (10 2 1 8) (6 11 3)
( 1 6 7 11) ( 8 3 10 5) (2 4 9)
(11 8 1 9) ( 6 2 3 7) (5 10 4)
( 2 10 7 11) ( 3 5 1 9) (4 8 6)
( 2 8 11 5) ( 4 3 1 7) (6 10 9)
