A few thoughts:
I don't know if ENT weighed in on this, but I seem to recall when Data was doing one of his verbal data-dumps about comparative views on mating that he said Andorians married in groups of 4. Trek Lit seems to have taken that ball and run with it to the idea that Andorians have 4 genders..
Having four genders doesn't necessarily mean four sexes... There ARE some cultures here on Earth where there are THREE genders.