Amanda, Cats are extremely sensitive to issues of territory and dominance. Are the 2 other cats female and younger? Older male cats are easily threatened by male cats of similar age but not usually by cats that are significantly younger (about 2 years or more in separation). In contrast, older female cats just beat up younger female cats and have an easier time dealing with competition. If the other cats are near in age to Shadow, then they all might be having problems sorting out who is dominant in certain areas. Male cats will spray in order to demonstrate their place in the hierarchy.

Cats oftentimes carve out different niches if they are close in age and of the same gender. For example, Cat A will be dominant in Rooms X and Y while Cat B may be dominant in Room X when Cat A is not present but Cat C is present and dominant in Room Z, etc. It can get really complicated. If the other cats are female and close in age to Shadow, they will try to exert dominance. This is generally ok if the cats all entered the house at similar times.

However, if Shadow was there for a long time before, he'll have a hard time adjusting to the fact that female cats of similar age always dominate. I'm sorry if this isn't clear - it's late and I'll try to do a little more research to see if there's a more linear explanation.