Yeah, I see how that could be annoying. Since there isn't a definite list, the best I can do is check everything manually within the HTML and see what comes out from there.
Currently, I don't see anything that can change the number of breasts a player has, or anything that checks how many breasts the player has. However, the number of breasts is stored, so there might be plans to do something with that in the future.
As for udders, there are technically 3 options: None (default), Cow, and Blob. "Blob" is the game's internal name for "Kindred of Grease", and you can gain the mutagen through eating Mystery Meat or letting the white jelly do its thing in the Caldera.
I don't think the player can change to match certain sexual encounters, and without the debug menu or save editing, there's no way to add or remove a penis or vagina to an already existing character.
For tails, you'll be relieved to hear that indeed, you can have multiple tails! This only applies for fox tails, and the status message changes as you gain more of them. In order to gain them efficiently, I think you can use Dreamweaving and focus on tails. The menu says it's unfinished, but I don't see any reason why it shouldn't work.