Be careful! Once you start reading Asimov’s stories you can’t quit.
If there were really three sexes, it could be quite confusing for the “gender” warriors. Consider the expression GLBT (my preferred way of expressing the more traditional LGBT). By my reckoning it would have to be modified to read — X1X2X3G1G2G3L1L2L3B1aB1bB1cB2aB2bB2cB3aB3bB3cT1aT1bT2aT2bT3aT3b*****++.
I will refer to the sexes as R = rational, E = emotional, and P = parental. A cis-hetero would be someone who prefers to merge simultaneously with one each of the two other sexes. A gay R could prefer another R (G1), an E only (G2) or a P only (G3); a similar configuration would apply from the perspective of each of the other two sexes (the “X’s” refer to homosexuals who are of the third sex). There would be three distinct types of homosexual orientation for each of the sexes. The “B’s” would refer to a member of any sex whose sexual preferences include any two or more of the above configurations. B refers to someone who is attracted to members of his/her/its/zis/shiz/hir/shir/their own sex and either of the other two sexes. B1a refers to an R who is simultaneously attracted to other R’s and E’s but not P’s. B1b refers to an R who is attracted to other R’s and to P’s but not E’s. An R who is attracted to another R and an E or an M, but not both at the same time, would be a B1c. B2’s and B3’s would follow similar patterns but from the perspective of each of the other two sexes. The “T’s” refer to someone who identifies as a sex other than his/her/its/zis/shiz/hir/shir/their birth sex. An R who identifies as an E would be a T1a; one who identifies as a P would be T1b. The T2’s and T3’s would refer to similar patterns from the perspective of each of the other two sexes. The string of *****++ represents other possible configurations that I am too lazy to try to work out.
Imagine how three sexes would complicate hook-up culture, rape culture or pick-up techniques. What would an exotic dance club look like? How would sex work be carried out? Which one would pay on a date? How would the hierarchy of oppression be organized? Or the progressive stack? Who would be expected to shut up, listen and believe? Would society be organized as a Ratioarchy? An Emotiarchy? A Parentiarchy?
While there can be as many “genders” as anyone wishes to invent, none of them are alternatives to the male and female sexes.
A continuum of sexes would mean that a myriad of people (one of each sex) would have to gather and copulate all at once if they wanted to conceive a child. That would be a sight to see.