Notes 1/ In order to have access to the books that are used in the production of an ngram (graph) click the underlined text of the research under the graph, or for only those books in a given period click that period.
2/ bold type has been added to all occurrences of "any more than".
This is not a definite answer; it aims at providing a general view of this usage and related ones, and is thus an introduction to further research. It is nevertheless a partial answer and those of my opinions that figure in it do so because they obtrusively impose themselves on my thinking, however, they should be taken as contentions to evaluate in the light of one's own judgement after it has been made solid.
I In order to use "less" there must be a positive verb form. Sentences constructed with "less" are rare in comparison to those constructed with "more" (and a negative verb) ngram.
ref. “And After Effex is Taryn's and my dream, Q, we've prepared for it. Just because we didn't go to college and don't have degrees saying we went to class for four years, doesn't mean we want it any less than you did.
In this usage there is not an underlying denial of the action ("it" is really wanted by both groups of protagonists in the sentence above) in a strict reading. This is not the case for "more" clauses and this will be explained below.
II
(SOED) any more To any greater extent; any longer.
This definition does not apply to the sentence in the post.
Not in those dictionaries: Cambridge, Word Reference, Collins, Merriam-Webster
- I don’t want to do this any more than you do.
I think it means "I don't want to do this either and considering what is the causes of your not wanting to do this there is none of them that's not a valid reason for me.
There is a similar usage for the verb "to like".
- I don't like it any more than you (do).
We find that it expresses a denial of the action: Word Reference.
This is a construction that is contradictory: strictly speaking it means "You like it, I like it too and the extent to which I like it is not greater than yours.". Instead of that, we are supposed to extract from it (roughly) "You don't like it and I don't like it.", which constitutes a breach of common sense really unacceptable. For this reason and the fact there are no references to this construction, I suspect it to be substandard.
Nevertheless, it is a recent usage that figures in the books since the 1950's (ngram). One strange constatation occurs in this research: the spelling is immaterial, "anymore" is found as well as "any more" (any more).
The construct "any more than" is used also as a support structure for plain comparisons and rhetorical comparisons (ref.), the resulting constructions being well established (ref.); the underlying meaning is not contradictory in this case.
ref. Even knowing you have it, does not make you value it any more than you did before you gained that knowledge.” “And Peter did? Valued his soul, I mean?” “He did, indeed.”
ref. Going to church doesn’t make you a Christian any more than going to a garage makes you an automobile.
It can therefore be confusing; in fact here is an instance where in the light of an exposition to what precedes, confusion becomes outstanding, if one may say so.
- I didn't drink any more than the guys did, but I got so much drunker.
The locution "any more than" can occur with the same contradictory meaning (if read strictly) in positive questions.
ref. He sagged a bit as the anger seemed to leave him all at once. “I know you are, but it's just so freaking embarrassing asking a woman I've never met about what kind of sex she had with a dead senator.” “You think I like it any more than you do?
