How hard is it to add to your family of pets?

I once had a middle aged cat about ten years old when my mom took on two abandoned kittens. He didn't know what to do with them as they rushed him to play. It took him a month before he sort of liked them but he never really was happy until they left. But then I had a rabbit who was a couple years old and we got a yellow labrador and they became best friends. My grandparents had a dog who would babysit the cat's kittens while they hunt so they met the dog when they were young. So it depends on what species, personalities, and ages you're mixing.

I find that cats need to have control of the situation. As long as they have a high place to view their domain and can get away from the other pet, they will learn to at least tolerate the new pet. Dogs need a moment to figure out they place in the new pack, whether it is alpha of the dogs, best friend of a rabbit, or babysitter of kittens. Rabbits, need a save place to dig and get away. Fish simply need non-aquatic animals to stop putting their paws in the water.