I just moved into a house that had a cat and dog, and I was worried about the same thing with my 3 and I already had 1 of them with litterbox issues. I bought a bottle of that 'Feliway' and used it like the instructions said and seems to have worked just fine, but I have no comparison data, i.e. what would have happened if I didn't use it. I had the carpets cleaned and cleaned all of the rubbing spots I could find. They adjusted just fine, the stairs and new noises took a little bit of work but they seem more comfortable less stressed now than they did in my other place.
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