Make sure everyone is up-to-date on vaccinations and that the new cat has had a thorough recent physical examination. You do not want to expose your cat to any diseases or parasites.
Confine the new cat to a room free of potential hazards, but that has food, water, bedding, toys and a litter pan available. Help establish a play relationship by attaching a toy to each end of a short string and running the string under the door; the cats may bat with the toy on their respective side and may even extend a paw under the door to entice each other to play.
Once all obvious signs of hostility are past, put the cats in carriers at opposite ends of a room for about half an hour daily. At that time, a special food treat could be placed in the carriers so they begin to associate the presence of the other cat with a pleasurable experience. If after about a week there is no hissing or growling, one cat could be kept in its carrier and one allowed to roam freely in the room. Be sure to rotate which cat is in the carrier and which is out, and secretly observe their behaviour so as not to influence their relationship with each other.
When they appear more interested in playing than fighting, allow them to be in the same room together while you are at home. Only after you are sure the new cat has been accepted should you leave them alone together.
Continue to leave out at least 1 litter box per cat (we recommend 1 extra too) to encourage good habits and prevent litterbox problems in the future.
While time-consuming, it is often well worth the effort to introduce the cats to each other slowly to ensure acceptance and peace among all your household’s inhabitants.