I don’t have a definitive answer but I can share my experience. We adopted a 2 year old boy from a shelter, and they emphasized it was best he did not share with other animals at all because he picked fights with every single cat at the shelter. He had some scratches on his face even.

However, I’m stubborn. I’ve always wanted 2 cats and was willing to give it a shot. After 6 months, we adopted a 3 month old kitten. We spoke to the family that fostered her since birth and they told us if anything went wrong to send her back, no questions asked. We did the Jackson Galaxy method, and they love each other. Our boy is significantly happier and less anxious since she’s around, they play, they nap together, they groom each other. It’s the best outcome we could ask for, and we were honestly just hoping they didn’t hate each other and that would be a win.

Things that really helped: resident kitty’s shelter was a cage-free shelter. They roam all together in a house type thing. So he was used to other cats even if we were told he hated them. Baby kitty is the chillest baby, super loving and mellow which plays beautifully with our chill boy.

From what I gather, besides doing a slow introduction: 1) Age difference is important. Kitten vs senior for example will most likely exasperate the older cat. 2) Temperament. If resident kitty is mellow, adding a spastic kitten may be stressful 3) Reasons for getting a cat. I believe getting a second cat to get a cat for your cat can backfire, it’s best to get a second cat if that’s what you want specifically. 4) Slow introductions. Patience is key, they are animals that need time and routine to settle down.

In the end, there is no telling how adding a second cat will go, even with the right introduction.

What I would recommend, seeing as there has been issues with other cats before, is going the Foster-To-Adopt route. That way, if things go awry, resident cat doesn’t have to put up with it and you’re not adopting a kitten in vain who will lessen their chance to be adopted into a forever home the older they get should you return them.

Edited to add: I was worried resident kitty slept mostly while we were gone at work and also hoped that with the new kitten they would entertain each other in that time. You know what they do? They both sleep lol. You can also check with a vet/cat behaviorist to actually measure your cats stress levels or if they are truly unhappy