don't be too quick to think that it is not physical. I had an inapropriate peeing problem last year (it was not spraying, it was always on the carpet, that is why I did not see the correlation). I had just introduced another cat myself and was 99% sure that was the problem. When we found out WHO it was (the hard part with multiples) we found out WHAT it was. Y.Lee had developed diabetes and could not make it to the litter box all the time (that is why I saw him in the box sometimes and did not think it could be him). The diabetes made him have to pee A LOT!!!! big puddles and too often for him to reach the boxes. And I am sure there are other physical things that could cause this. Don't give up.