There is another model organism that is famous for being androdioecious: C elegans. Nematodes use an X0 sex genetic sex determination system where males have only one X chromosome, XX makes a hermaphrodite, and there are no females. Androdioecy, this strange reproductive system with only males and hermaphrodite, is rather rare and it is unclear how it arises during evolution. Yet it has evolved independently multiple times. In triops, It usually reaches an equilibrium with a large majority of hermaphrodites and a few males. As you can imagine, since the male only invests energy into producing sperm, they can fertilize much more eggs and produce more offspring than the hermaphrodite. However, if the population of males becomes too large, then each encounter with a male is a lost opportunity.
This reproductive strategy has the advantage that only 2 organism suffice to have a threesome. It does however come short of this pair of humans with supernumerary sex organs which managed to simultaneously have sex twice over:
"Blanche Dumas was born on the Caribbean island of Martinique in 1860, to a French father and a biracial mother. She had a third leg attached to her sacrum, and her two primary legs were said to be imperfectly developed. The third leg was without a mobile joint but had a bend in it where the knee would have been. Her pelvis was wider than normal and she had double genitalia as well as a duplicate bowel and bladder. Most remarkably, Blanche had two small rudimentary breasts situated at the junction of the parasitic twin with her own body. Each had a nipple, but they were non-functional. Stories of Blanche all mention her pronounced libido. She moved to Paris later in life and became a courtesan, and allegedly, upon hearing about the three-legged man, dos Santos, who was touring at the same time, she expressed a desire to have sex with him. According to Gould and Pyle, "There were two vaginae and two well-developed vulvae, both having equally developed sensations. The sexual appetite was markedly developed, and coitus was practised in both vaginae."