In the TV series Alien Nation there were three genders, but only two provided genetic information. the third had to provided something like a "catalyst" if the married pair wanted to conceive. The third gender was not part of the family group, the couple would basically arrange a "date" with him when they were ready. The third gender was somewhat rare and usually very popular.
In the case of the Andorians add another gender who just carries and that makes four.