Is it possible that there could be more than two sexes in an alien species

On earth there are a number of organisms that have more that two sexes. So if there is life on other plants, there is no reseon that it too could not have multiple sexes also.

If there is life with a complex body structure (multi-celled with organs) on other plants, chemically it is most likely if not necessary that it would be organic based, and two sexes would be the most efficient means to produce genetic diversity by means of sexual reproduction. The entire purpose of sexuality is genetic diversity, multi-sexes would ensure the greatest diversity but also could be a limiting condition in mate selection.

If more than two gametes fused to form a zygote, you could have one sex per gamete needed. There are single celled organisms, particularly fungi, in which there are numerous mating types, gametes which can fuse with any type other than the same type. All animals, even sponges, form heterogametes, one large (ovum), one small (sperm, even if not flagellated). That is what defines two sexes, even in hermaphrodites. The mechanics of reproduction are immensely varied on that theme, such as sea horses where the males carry the young. Freed of the constraints of Earth's natural history and able to construct one of your own, anything is possible.

The Pierson's Puppeteers from Larry Niven's "Known Space" stories had a pseudo-three-sex configuartion. A separate species which reproduced independently was the third sex--not so far off from flowers which require another species to pollinate them.

Of course, if we want to speculate that their are aliens, whose to say whether or not there might be more than 2 sexes.

I read in a scifi novel once where there was some organism that had 3 sexes... 2 supplied genetic material to the 3rd, which incubated the progeny and may or may not have contributed genetic material... so who knows... it's not impossible.

On Saturn the sexes are three
which is awkward I think you'll agree
for performing con brio
you must have a trio
and it even takes two for a pee

(Attributed to "Dr. A" Isaac Asimov)