Zealous,
No, I don't think you can. It seems that the reason that many schools consider appeals is that often only one person makes the initial decision on your application. After you interview the entire committee discusses you. If only one person looks at your application, it is possible that a "mistake" could be made (maybe that person has a personal bias against people like you or missed something in the application). It is unlikely that the committee will miss something since it is a larger group of people and you have personally interviewed with someone.