Bringing home a pet to an empty house is pretty easy because you just have to get the pet used to its new home. However, bringing a pet into a house already filled with pets can be more stressful because now the new pet needs to get along with the current ones already there.
As a general rule, introduce the new pet slowly over a period of days or even weeks. Make sure each pet has its own space and let them smell the other pets so they get familiar with them. Eventually, let the cats see each other and then pray that everything goes well, which is the usually way to behave with cats in most situations.