Stealers Wheel's "Stuck in the Middle with You"

A couple months ago, I happened to hear Stealers Wheel's "Stuck in the Middle with You" on the radio, and I thought I noticed something.  I listened to it recently for my Collection Audit project, and I confirmed what I thought I heard back then.  Every occurrence of the titular "stuck in the middle with you" line has a vocal harmony part.  There are two voices there to musically represent both the singer/speaker and the "you" he's stuck with.