This is in relation to both the Sword of Truth and the Legend of the Seeker universes. I have only seen the tv-series, but I'm interested in an answer drawing from the books canon.
The question is really simple, as stated in the title: What happens if a Confessor tries to Confess an already Confessed person?
Logically, there are two possibilities: (1) nothing happens, (2) the previous Confession is reversed in favor of the new one. Of course, something else like (3) the person dies / becomes mad, can happen as well, but it's just guesswork.
I do not remember any such attempts made in the LotS, mainly because seldom we had more than one Confessor in the scene.
On the other hand, at least in one instance, it would have been really useful, namely when Richard was Confessed by a young girl (the episode "Touched") and Kahlan's immediate reaction was to try and kill her.