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then we moved house and they bonded over a new territory and now they're best mates.
This is a good point - it will have worked because there was no territory in the new place already staked out, and they'll have needed to negotiate it between themselves. That's a lot easier than Cat #1 being the Lord of All He Surveys for n years and then suddenly there's a Cat #2 sitting in his favourite room and using his litter box and getting all the pats that were rightfully his. No wonder the poor little furry bastards get angry.
If Basil has access to outside when you're at work he probably doesn't care much about being left alone all day as he'll have cat things to be getting on with. But if he's an indoor cat or he only gets to go outside when you're home then he'd probably appreciate things in the house to climb over and jump off if you don't have much by way of cat entertainment - they like clambering up things more than they like pawing at stationary toys on the floor. Cat shelves with bits of carpet stuck to them and that sort of thing. Bonus is that if you do end up getting another one then with a good cat climbing system there'd be places for Basil to go and hide in while he comes to terms with what's happened.
Opie and Gomez hated each other for while, then we moved house and they bonded over a new territory and now they're best mates.
Gomez hates cars.