There are many styles of portrait photography and each subject and/or project requires a certain feel. For me, the studio set up should not always be the go-to style. A portrait is supposed to capture the person, and a part of their essence, what makes them who they are. So for example, in my portfolio here you will see that for the corporate head shots, I find that on-site, at work portraits say a lot more about the person that a flat background that is used in the majority of portrait photography.
The same is true for pets, if thought is put in, then the pet's personality can be captured.