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Basil is very friendly and is castrated, but just to be sure..
There's no way to be sure, and Basil's friendliness with humans and his genital status doesn't make a huge difference to how he'll interact with another cat. Basil will see it as an imposition on his territory, and the new cat will see it as a terrifying experience akin to being dropped into the middle of the Predator jungle with only a jungle knife for survival. They're 90% likely to really fucking hate each other in the beginning, but will probably come to tolerate each other. In some cases they'll never come to like each other much, and will try to ignore each other as much as they can, with occasional fisticuffs. Sometimes they will engage in little wars against each other that you might not even notice are happening. Some cats who were littermates end up hating each other, for absolutely no reason at all, even when they've spent their entire lives together. It's really unusual for introduced cats to become friends (but it does happen!)
Generally speaking I'm against the idea of getting a second cat for the benefit of an existing cat, unless you've got a bloody good reason for doing it. It's a hugely stressful event for a cat, and not at all like it is with a dog, dogs love that shit. Cats are independent and territorial. If you really must do it then you'll probably get better results with a (neutered, obvs) kitten of the opposite sex. But do think about why you're doing it, really - Basil will not be thrilled with his new friend, even if you and your girlfriend are.
So we're thinking of getting a little buddy for Basil, our 2 year Bengal cross (the twin of @c0gsucker 's Opie, by the looks of things). GF is pretty keen on a Tonkinese, my only worry is how Basil will take to it. What are people's experiences around bringing 2nd cats into homes? Basil is very friendly and is castrated, but just to be sure..