Bringing another cat home is a wonderfully loving thing to do, but it will put quite a bit of stress onto any existing animals in the home. To lower the stress level and make this transition period as amicable as possible, you are going to need to introduce the new cat into the household in a slow and gradual process.
To begin, separate the new cat from any existing pets in the home by putting them in separate rooms for about a week. Let them sniff each other out under the door, where they can familiarize themselves with each other without feeling threatened in any way. This gives them an opportunity to introduce themselves at their own pace. This also allows the new cat to become accustomed to new surroundings and creates a sense of security.
Change rooms so each pet has an opportunity in the other’s room. This allows further familiarization with the others scent and lets everyone know that there are additional pets in the home.
Open the doors so the new cat and the existing cat or other pets are able to see each other and put a visual to the smell. There may be some hissing, growling, or other various noises but unless one becomes extremely agitated, this will pass in time. Continue letting them see each other for brief periods throughout the day, but do not let them near each other yet. Also, continue switching rooms so they will recognize the scent with the animal.
Let the cats come together, for longer periods of time each day. A great way to establish a relationship between them is to play with them together. They may not play with each other, but they will both play with you and discover that you possess a shared love for all of them. Dole out treats and cuddles in equal amounts so no one feels threatened that there is now new competition.
Allow longer and longer play periods together, and let them explore each other without your intervention.
Generally, this process takes anywhere between two to four weeks, depending on the age and personalities of your pets. However much you ease the transition, it is part of the animal world to create their own hierarchy. You can now build your relationship with your new cat without your other pet’s feeling jealous; however, some cats never completely get along together with other pets, but will usually tolerate each others company.