My stab at the artist who appeared 3 times in one TOTP would be.....
Gary Tibbs!
Who? I hear you cry....
Well Gary Tibbs was a bass player who was in both Roxy Music and Adam and the Ants at the same time in the early 80's. He also played bass with Hazel O'Connor and featured in the film Breaking Glass.
So I reckon it is conceivable that on one TOTP, in 1981, he could have played on:
Hazel O'Connor - Eighth Day
Adam and the Ants - Stand and Deliver
Roxy Music - Oh Yeah
Now, even though I suspect this is probably wrong, I would like some major nerdy respect for knowing this sort of crap!
Alternatively, we could be talking about a Xmas TOTP in which George Michael could have featured solo, in Wham and in Band Aid???