Sounds much like the background on the alien-of-the-week from the episode Cogenitor.
There is also a fascinating and extensive extrapolation of the Andorian race from the 70s by fanfic/filksong writer, Leslie Fish:
http://andorfiles.blogspot.com/2009/09/summary-of-physiological-roots-of.html
The DS9 Relaunch was not at liberty to use her material, of course (although two TNG novels, "Metamorphosis" and "The Eyes of the Beholder", did use a few references from her work), but the Pocket editors were aware that Ms Fish had postulated
three Andorian sexes. (It is also possible that Data's line in TNG made use of "fanon" that Andorians had a different reproductive cycle than most other humanoids.)
Fish's Andorians are born male or female and pass through a "neuter" stage. Fertilization for reproduction is similar to seahorses, with males carrying the embryo for some time. In one of her fanfics about TAS Andorian, Mr Thelin ("Yesteryear"), she connects him to seemingly-male Ambassador Shras of "Journey to Babel" (TOS), whom Thelin refers to as his "Aunt Shras".
The other big difference between Fish's material and the DS9 Relaunch Andorians is that Fish blames chronic overpopulation for Andorians' warrior culture, while DS9 novels say that Andor is suffering from underpopulation which will lead to extinction if the problems of a four-sex paradigm can't be resolved.
BTW, a recent ST novel has suggested that greyish Mr Thelin (miscolored in TAS due to the colorblind director - the script specified he should be blue) was part
Aenar.
One would assume that it would be difficult for a non-Andorian to conceive with a single Andorian...
Captain Lisa Cusak, late of the
USS Olympia, tells the
USS Defiant crew that she was once in a (presumed childless) relationship with an Andorian civilian for six years. He was working on Andor with the Agricultural Ministry and disconcerted her, at their first meetings, by always pointing his antennae at her ("The Sound of Her Voice", DS9).