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Is she stressed about the other cat? Is she neutered? I think you ought to give her vet a call see if they have any proper suggestions? My experience with vet is that they are usually pretty good with giving free advice on the phone anyway. If not, if she is from a cat home, give them a call and see what they can suggest?
Sorry not really answering your question, but I do think there is a territory marking thing.
In my house live 2 dogs and 2 cats. Generally the dogs live downstairs and the cats live upstairs. One of the cats (lets call her "Tilly") just pisses where and when she feels like it. On our bed. On anything left on the floor. In bags. At least once a week, sometimes more.
Either the pissing must stop or the cat must go. I'm fed up with living inside an animal toilet. Any suggestions for either route very welcome.
Notes:
we've tried Feliway with no success
The cat doesn't seem to care about the dogs or be stressed at all. She just likes pissing on things :(