Here is the 33 player whist, which has 33 rounds (rows) and has all partners once and all opponents twice. Similar balance for 34 players would be impossible.
[(16 12):( 5 13)] [(21 33):(14 3)] [(19 27):( 4 31)] [(22 28):(23 2)] [( 9 15):(24 18)] [(26 7):(29 11)] [( 6 10):( 8 25)] [(17 32):(20 30)]
[(32 19):( 7 11)] [(18 17):(21 26)] [(10 24):(22 2)] [( 3 23):( 6 14)] [( 1 8):(25 29)] [( 5 30):(31 9)] [(15 12):( 4 16)] [(27 20):(33 28)]
[(20 19):(29 30)] [( 2 16):(23 1)] [( 5 4):(28 11)] [(25 9):(14 27)] [(10 3):( 6 18)] [( 8 22):(32 33)] [(21 7):(26 15)] [(24 17):(13 31)]
[(19 23):( 7 9)] [(31 14):(29 10)] [(13 17):(25 18)] [( 4 8):(16 15)] [(27 24):(26 20)] [(33 3):(12 22)] [( 1 5):(32 11)] [(28 6):(21 30)]
[(26 13):(10 27)] [( 6 8):(15 30)] [(11 14):(24 20)] [( 9 22):(18 21)] [(33 29):(23 16)] [( 4 12):(32 2)] [(25 1):(31 3)] [(28 5):( 7 19)]
[(33 6):(28 25)] [( 4 2):( 8 7)] [(15 3):(19 13)] [( 5 26):(29 18)] [(11 10):(32 24)] [( 1 16):(30 14)] [(12 20):(31 22)] [(23 17):(27 21)]
[( 1 21):(27 15)] [(26 33):( 5 9)] [(28 19):(18 16)] [( 8 3):(20 32)] [(31 10):(22 7)] [(17 2):(12 29)] [( 4 14):(30 24)] [(25 13):(11 23)]
[(26 1):(25 10)] [(28 23):(14 20)] [( 8 29):(12 17)] [(19 30):( 2 27)] [(11 6):(31 21)] [( 3 5):(15 13)] [(22 4):(18 9)] [(32 7):(33 16)]
[(24 28):( 8 17)] [( 9 29):(25 12)] [(27 22):(20 5)] [( 2 11):(15 6)] [( 7 16):(21 3)] [(31 1):(26 14)] [(23 33):(32 18)] [(19 4):(10 13)]
[(21 32):(27 29)] [(12 3):(10 28)] [(31 5):( 6 9)] [(24 4):(30 7)] [(25 19):(33 13)] [(14 18):(11 20)] [( 1 15):(22 17)] [(26 2):(23 8)]
[(14 16):(17 15)] [(10 23):( 4 30)] [(22 11):(29 26)] [( 7 5):(31 8)] [(20 1):( 9 12)] [(28 21):(13 32)] [(19 33):(24 6)] [( 2 18):( 3 27)]
[( 9 4):( 3 24)] [(30 2):(28 32)] [(10 33):(18 15)] [(27 17):(12 7)] [(29 14):(13 22)] [( 6 1):(23 26)] [(19 8):(21 11)] [(16 5):(20 25)]
[(17 6):(24 14)] [( 3 20):(26 11)] [(21 25):(30 12)] [(32 16):(18 23)] [(29 4):(19 5)] [(33 27):(10 15)] [( 8 28):( 7 31)] [(13 2):( 9 1)]
[( 6 26):(28 16)] [( 1 18):(24 19)] [( 9 2):(32 4)] [(12 10):(20 31)] [( 7 17):(23 13)] [(27 5):(22 15)] [(33 25):(11 30)] [( 8 14):(21 29)]
[(12 23):(11 18)] [(32 1):(20 6)] [(27 28):( 3 29)] [(26 16):(24 31)] [(14 33):( 4 7)] [(30 8):(13 9)] [( 5 2):(17 10)] [(15 19):(22 25)]
[(31 28):(33 22)] [(23 32):( 3 13)] [( 7 10):(14 9)] [(16 25):(21 2)] [(15 8):(12 26)] [(20 17):( 4 6)] [( 5 29):(18 30)] [(11 24):( 1 27)]
[(22 26):(25 4)] [(17 29):(33 11)] [( 5 24):(23 21)] [( 7 20):(13 1)] [(12 28):(18 27)] [(14 10):( 9 16)] [( 2 19):(30 3)] [(31 6):(15 32)]
[(11 8):(23 31)] [(30 16):( 7 27)] [(21 6):( 4 20)] [(10 5):(17 33)] [(15 28):( 1 19)] [( 2 3):(22 24)] [(12 18):(14 13)] [(25 26):(32 9)]
[(18 33):(31 30)] [(11 15):( 9 10)] [(17 19):(32 26)] [(27 13):( 6 22)] [( 5 25):(14 23)] [(29 24):( 3 28)] [(16 21):( 2 20)] [(12 8):( 4 1)]
[( 1 14):( 4 27)] [(16 19):(25 31)] [( 2 6):(33 7)] [(29 15):(23 9)] [(30 32):(18 26)] [( 5 21):(24 13)] [( 3 17):(20 8)] [(12 11):(22 10)]
[( 4 17):( 3 1)] [( 6 7):(22 18)] [(13 28):(31 32)] [(11 19):(21 14)] [(20 15):( 2 25)] [( 8 10):(16 27)] [(29 23):( 9 24)] [( 5 12):(30 26)]
[(15 5):(14 32)] [(13 8):( 1 22)] [(20 10):(25 23)] [(33 24):(19 12)] [(30 27):( 3 11)] [( 2 7):( 6 29)] [( 9 28):(17 16)] [( 4 21):(18 31)]
[(19 3):( 9 8)] [(20 13):(33 15)] [(26 31):( 2 14)] [( 1 24):( 5 32)] [(21 17):(10 30)] [(11 25):(28 4)] [(27 12):( 7 23)] [( 6 16):(29 22)]
[( 2 29):(13 18)] [( 7 25):( 5 17)] [( 8 32):(14 22)] [( 4 26):(33 20)] [( 6 30):(24 12)] [(19 31):(27 23)] [(10 21):(28 1)] [( 9 3):(16 11)]
[(13 21):(10 2)] [(16 24):(32 22)] [(17 30):(23 15)] [( 3 25):(31 29)] [(28 20):( 8 5)] [( 7 18):( 1 11)] [(33 4):(26 27)] [(19 9):( 6 12)]
[(22 3):(30 25)] [(31 12):(24 21)] [(16 8):(11 27)] [(10 4):(32 29)] [( 2 1):( 5 33)] [(19 6):(17 26)] [(13 7):(20 9)] [(18 28):(14 15)]
[(18 20):( 2 31)] [(19 26):(12 14)] [(24 7):(15 25)] [( 1 10):(28 30)] [(17 11):(16 22)] [( 9 33):(21 8)] [( 6 27):(13 29)] [( 5 23):( 3 4)]
[(32 12):(15 7)] [( 2 24):(27 25)] [(26 8):(30 13)] [( 9 11):(28 17)] [(22 21):( 4 23)] [(16 20):(18 19)] [(14 5):( 3 6)] [(31 33):( 1 29)]
[( 8 33):(23 24)] [(19 21):(22 5)] [( 1 30):(29 16)] [(13 12):(14 28)] [(27 9):(32 6)] [(18 4):(25 17)] [(15 2):(11 31)] [(26 10):( 7 3)]
[(12 2):( 5 11)] [(29 28):(15 4)] [( 1 33):( 9 21)] [(25 6):( 8 18)] [( 3 32):(17 31)] [(10 19):(20 23)] [(24 26):(16 13)] [(14 7):(30 22)]
[(20 22):(30 9)] [(18 5):( 8 27)] [( 6 23):(12 1)] [(26 3):(15 21)] [(16 31):(13 4)] [( 7 28):(24 25)] [(29 19):(10 32)] [(17 14):( 2 33)]
[( 6 5):(16 10)] [(27 31):(17 9)] [( 7 1):( 3 18)] [(11 13):(30 33)] [( 8 2):(19 14)] [(21 12):(25 32)] [(23 22):(28 26)] [(24 15):(29 20)]
[(21 20):(29 7)] [(11 4):(13 6)] [(16 3):(33 12)] [(22 19):(17 1)] [(28 2):(26 9)] [(23 30):(15 31)] [(25 14):(27 32)] [(10 18):( 8 24)]
