Genders?
Of course there are more than 2 genders. Gender is a grammatical term... masculine, feminine, neuter, common, etc.
There are 3 sexes: male, female and hermaphrodite. That's a simple matter of anatomy.
Gender: a social construct
Sexes: typically as you say, but with complication due to various chromosomal syndroms.
There are XX who are males, there are XY who are females (due to SRY gene mutation).
Typically, though, a presence of Y chromosome is a strong inducer of masculinity. For example, even XXXY are mostly males.
List of syndromes:
https://en.wikipedia.org/wiki/Sex_chromosome_anomalies_________
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