Succubus transformation is earliest available via the Devil Candy in Alisha's house. They're in a treasure chest in an optional room, past a switches-and-launchpad-tiles obstacle course. I think once you've used one and thereby added the Succubus status to the journal, the Traveler starts selling Candies too. It's quite useful for actual gameplay; its spell set uses the Lust meter as a mana source rather than a limited number of charges, and the Masturbate command is available anytime out of combat so you can replenish it between fights-- or even heal ally HP (Sultry Heal) and eliminate built-up ally Lust (Edge). They can also still use conventional limited-charges magic if the character already knew them from another class. Luxatep's dress is perfect for a Succubus (Arousal status means continually regaining Lust to cast spells with!), and they can also equip the same Tattoos as Bimbos can.The transformations overall felt disappointing to me too. I was hoping for more stuff like breast expansion, cock growth, the girls getting turned into a monster girl or a furry, I dunno. More stuff that also kept the character's "agency" or "mind" intact while still changing them outwardly. Instead a lot of the fetish content featured is a lot more mental alterations and whatnot. I read about a succubus transformation and while it sounds great, I don't necessarily want to keep playing just for that.
Orc transformation (includes futa since all Orcs are futa in this setting) becomes available after you finish Tabnath, I think; you get a reusable scroll in your key items that inflicts the status. (I think the Mystery Dish can also have "inflict Orc" as its effect, possibly without even getting the scroll first.) Its skillset has some overlap with the three Combat characters; in fact, you can save some Elixirs on them by having them learn the overlapping skills with Orc JP instead of main-class JP.
Cow transformation might be the closest to furry, though it does also eliminate the affected character's agency. I guess this is another way to make use of the Lost Wizard.