No. of Recommendations: 2
There's no "Extra Limb Syndrome."
BTW, as punishment for trying to come up with an interesting analogy, I have just found that in exceptionally rare cases, people who have suffered brain injuries or strokes or other trauma to certain parts of the brain will report supernumerary phantom limb syndrome. Where they will (often temporarily) report the sensation of having an additional limb, and even experience some sensorimotor activity corresponding to that limb. It's a very interesting world we live in.
So amend my illustration to be something that doesn't exist - say, "Second Head Syndrome." The point is still the same - we are dealing with the question of what psychological conditions actually exist in the world, not the question of whether one thing is reasonable and the other is absurd.