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Wonder if anyone has experience of cats behaviour and any way of increasing the likely hood that the two will get along.
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My experience is that when another cat is introduced into a household they merely tolerate each other.

Hmmm. Initially H had two cats. Twin brothers. Almost impossible to tell apart. Went everywhere together, inseparable. Up on roofs, chased of other cats, ran the roost, and pretty much did as they pleased.

Then one was hit by a car, tother withdrew totally so H got another cat, Masey, (she's got her nose in my ear as I type)

to bring him out of himself. Which worked.
Except he completely ignored Masey. Never acknowledged her at all, and I suspect took a lump or two out of her when we where away.
Masey is the mothering sort, mischievous but always gentle. She always wanted his attention, and got frustrated when he ignored her. So I suspect she will be fine with any cat.
We just need to find another cat that will be fine with her. I suspect another female will be better, as males alway want to dominate as they get older. Even between mother and son, as I found when I was younger and our female had kittens.