Cats need to be properly introduced to the new home, the new humans, and the existing cats if they are to get along well and not have problems.
Here's how we introduce newcomers to our gang:
Cats need to be introduced very slowly.
First of all, we do not allow a new cat to have any contact with our other cats until a vet has given the new cat a clean bill of health. This includes tests for such things as FIP and Feline Leukemia.
Cats can be successfully introduced to each other regardless of their ages or sexes.
We have successfully added adult cats to our family containing both young and old cats as well as introducing very young kittens to the other cats.
It has to be done slowly. If you simply put them together, you will have behavioral problems the vast majority of times.
The new cat has to be given time to get used to you and the new environment - don't try to introduce the new cat to the new home, to you, and to the other cats all at once. Do it in stages.
Also, the existing cat has to get used to the smell of the new cat.
We introduce cats by keeping the new cat in the back room for up to a month. My office is there as is my wife's sewing table. There is a sofa and bookshelves.
We spend a lot of time with the new cat to get them used to us, the new environment and the new smells.
After they accept us with no problems, we put a screen door on the back room door frame and let everyone see each other for a week or so.
It may take a lot less time than a month to get to this point but we just take it slow and easy.
Once we judge it safe to do so, we let the new cats out into the house and chaperon the first encounters.
We've only ever had one problem introducing cats like this and that problem was resolved in a couple of weeks.
We've had 26 cats over the past 22 years and many of them were adults - 12 and older - when they joined our family.
We've also introduced several kittens, ranging from ages of 7 weeks to 4 or 5 months, to the rest of the crew with no problems.
You have to take it slow.
If you can't put up a screen door, perhaps two baby gates, stacked one on top of the other, will close off the door but still allow the cats to see each other.
If you can't use a screen door or baby gates, try letting the existing cat into the room with the new cat for a few minutes while you chaperon.
If things get bad, take the cat out of the room.
You just have to introduce cats slowly
There are cats who could be thrown together and become pals but they are few and far between.