You do over time receive 1 of each over the course of a few days in story 2, there are a few ways to keep them too from story 1.
during your stay on the ship, you can corrupt the crew, as you corrupt them you will gain more options specificially the captain, when shes been corrupted by a parasite to the brain (via the neck brace), you can go to the station and gain access to the star parasites, after that you basically have all the parasites.
slap them onto the crew not the station crew (honestly they are irrelevant unless you want some artwork and some extra parasite spawners.
after a few moments over time visit the crew and they will spawn 1 of each (if you have infected them with each one).
This can be repeated as many times as you want (put an egg in them etc etc) rinse repeat, collect an abundance, then leave via the ships escape pod to keep the parasites, if you leave via the station and the parasite choice exit you lose them all and have to start from day 1 waiting or corrupting the woman in the bathroom (when you go to school she asks if your a lesbian say yes every time).