I don't know about cats, but both my parents and my sister have a bunch of dogs that don't get on and have huge, bloody fights. The general consensus is to separate them. You can put a girl and a boy together, but not two girls and two boys. So they have one boy-girl pair in the front yard and another boy-girl pair in the back yard. My sister had to divide her yard.
One of the points in this book is the difference between dog and cat interactions with their own species. Cats do need their own space in a house, whether they get on or not, but it's a different mentality. Their more primitive instincts are very solitary where dogs are descended from pack animals.
Read a dog book recently and apparently dogs are more interested in people than other dogs (even the ones they live with). I suspect each animal is different, has their own personalities and their own needs.