Unlike humans and dogs, which have a wide array of behaviors meant to diffuse a tense confrontation and de-escalate it, cats do not. Humans smile, and dogs yawn to calm others down. Cats really just have a few things they do in a confrontation, and none of them are de-escalating behaviors. They will stare another cat down. Their ears go down and the body tenses. They will yowl endlessly while facing off with another cat. You’ve probably heard that yowling sound in your backyard in the summer. If neither cat backs down, one or both of them will hiss, bat, swat and possibly bite.
To acclimate your new cat or kitten to the household, start with the newcomer cat in its own room with the door closed for 24 hours. Let the cats sniff each other under the door. Make sure the new cat has been to the veterinarian for a physical examination, worming and has been vaccinated and checked for the absence of fleas, feline leukemia virus and feline immunodeficiency virus (FIV). Make sure you have one more litter box than you have cats. Two cats require three litter boxes in different private spots all around the house. The boxes cannot all be in the basement. They must have separate water and food bowls, and those must not be in the same area of the house. They need excellent hiding spots and vertical height to climb and exercise. They need enough space so they can decide to be social or be by themselves.
When you let the two cats meet each other, make sure to have lots of treats, toys, attention and exercise for both of them. You may want to bring the new cat out of its room several times a week for these short 5- to 15-minute sessions. Then, on a day you can observe most of the day, let the new cat out.