Assuming we're working with genetic transfer, and not something like crystallized memories, spiritual inheritance, etc. gender identities don't really count as those are societal and neither should the aforementioned example of a pheromone bearer as that doesn't actually involve the blending of genetic data. (And, to carry the example of 'organized involved in, but not contributing to' reproductive habits, that would mean that bees are a third sex to who knows how many plants...)
As it is, I'm seeing limited use for an evolutionary cause for a third sex. On one end, you have a single sex that tends to undergo genetic modification through chance or copying defects. With two, you have a good chance of diversity without it being overly difficult to find a partner. With greater numbers, the complexity of reproduction rises and the amount of genetic drift. But just what kind of pressure would splinter off a even more sexes? The kind of things that would induce that, in my amateur opinion, are more likely to render a species extinct or bring about extreme dimorphism (I feel bad for male angler fish...). (There're also probably various chemical reasons why you wouldn't see much in the way of tri+-nodal genetic material, though I can't speak on that at all.)
However, this can be largely waved away through existing lore: "Avian numbers were beginning to dwindle when a superior race took pity and bestowed the gift of advanced technology upon them." Numbers could've been beginning to dwindle due to reproductive problems and one of the things introduced to them is cloning (with any number of individuals involved!... within reason. There's only so much genetic material an individual needs.) or some other tweak to their systems. Maybe they were all made hermaphroditic. Solves a lot of problems that way.
(Which, now that I think about it, I wonder why hermaphrodites aren't seen more often. Well, looking that up will keep me occupied all night.)