I would not be surprised if you could find some zoos that even today are keeping all five Panthera species.
Just to be clear, there are 6 species in Panthera, of which no zoo has all 6....
Parc des Felins somewhat outdoes every other zoo in the world on this count, with a stunning 13 Panthera taxa:
Amur leopard
Asiatic lion
Barbary lion
Indochinese clouded leopard
Jaguar
Malayan tiger
Persian leopard
Siberian tiger
Snow leopard
Southeast African lion
Southwest African lion
Sri Lankan leopard
Sumatran tiger.
Still not all six species though...
SDZ does and also houses clouded leopard, mountain lion, and cheetah if you count those as "big cats."
Not going to get into this discussion again, but clouded leopards are objectively big cats and mountain lions and cheetahs are absolutely not