We might have a cat incompatibility problem. We can solve it with… a Third Cat.
To make our cementing Third Cat block more sturdy, we should make this cat a carefully chosen move:

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The right sex. When choosing First Cat, it doesn’t matter. Maybe we didn’t have a choice with Second Cat, or we feel we must have chosen badly for the situation to have turned out the way it did.
While their sex doesn’t matter for their suitability as pets, it does have an influence on inter-cat relations. I’ve found that cats are more likely to be buddies if they are the same sex.
There are certainly all kinds of exceptions; opposite sex cats can be friends. But if we are working to remove barriers to compatibility, a same sex match can give us a bit of an edge.
The right type. With widely varying types, we can use Third Cat to split the difference.
But a such a move is not always the best choice. We can love the sweet Persian mixes, but wind up with two cats who cannot make social connections. This may result in the two cats ignoring each other, which isn’t too much of a problem.
But if one cat is lonely, they will keep asking the other cat for friendship. The lonely cat will be upset that they keep getting rejected. The solitary cat will be upset that they keep getting asked.
In this case, getting another Gamma would help the situation because their style is not so different from the other cats. But deliberately getting a mellow, highly socialized Gamma will create an optimum situation for the lonely cat, while modeling better skills for the solitary cat that they can take advantage of… or not. It will be up to them, finally, because the lonely cat will find buddy opportunities with Third Cat.
And we get three cats of our favorite type.
Or we might have an Alpha who is just too much for an older or quieter Beta, straining their coping abilities. The Alpha is the one who needs more play and more interaction; getting another Alpha would be the right choice.
The right age/activity level. Age/activity is like a fine-tuning knob on our cat choice. A baby Beta has the energy to keep up with an older Alpha, while an older Beta can be just right for a baby Gamma.
Kittens have a built-in advantage when it comes to being Third Cat. They are less sensitive to rejection, are still building their social skills and can be more forgiving of social blunders, and are less likely to trigger territorial imperatives.
Just look at them! Older cats usually have an instinctual understanding that such bumbling foolishness is not trying to take over their territory.
But kitten ease comes with a built-in disadvantage, too. They are high-energy; they must have a target who will accept the sudden pouncing and ritual disemboweling that kittens will perform on them, whether they like it or not.
Bringing a kitten into a home with two older cats might mean two cats getting harassed, and neither of them liking it. The way around that, of course, is to get two kittens. They will play with each other, and can band the two older cats together in mutual disdain of these little beanheads.
This also means doubling our chances of the kittens being the right kind of cat to win over one or more of the older cats.
If such a move gives us pause, we should consider an under-three. We are upping the territory imperative somewhat, but we are also lowering the pedal-to-the-metal exuberance that can so distress quieter cats. Under-threes combine kitten friendliness with more mature sensibilities; they are more able to take their time making friends.
Older cats are less flexible; both physically and mentally. If we have two older cats who don’t get along, and their combined age is greater than ten, we might consider a different step: re-introduction of these two cats.
If we make this move successfully, we can more easily consider a Third Cat.
Yes, it’s true. I’m saying:
The solution to your cat problem is more cats!
Because so many cat problems arise from cat incompatibility; which is usually from cats reaching out, and being rebuffed. If we take care of the social reach of the lonely cat, we also take care of the harassment problems of the solitary cat.
Giving everyone what they need. That’s how any happy family gets built.
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There’s more to choosing a cat with The Way of Cats than the article you are reading now. See my CHOOSING A CAT.