I think the first girl in Dan the Barbarian has one like this? The girl who turns into an elf after Dan makes his first wish. First girl in the harem.
Either way, Dan the Barbarian is a great series, and you should read it.
Here's a start:
Hondo Jinx - Dan the Barbarian - Harem isn't too special, grey elf, blood (red) elf, werewolf chick. That said, at the end of book 3, it introduces a naga, a pixie?, a gargoyle, a panther morph, and a few other females at the end after doing the plot related stuff (no spoilers). Its a really good series, and doesn't spend too much time moping. I'd say some nice plot development.
https://www.amazon.com/Dan-Barbarian-Gamelit-Fantasy-Adventure-ebook/dp/B07FYXKNZM
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Jan Stryvant (pen name of John Van Stry) - Valen's Legacy. MC becomes a werelion, manages a were army, and has different wives of several species (two-three are weres). Is in fact litrpg, as he checks his stats and applies points, though the story doesn't actually track numbers. Much nicer to read than spreadsheets.
https://www.amazon.com/Jan-Stryvant/e/B06ZY7L62L/
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John Van Stry - Portals Series. MC is teleported to another world where he becomes a champion of a god to do his dirty work. Becomes a cat person (can't remember actual race). Travels to other dimensions and worlds, fights in his champion form, which is tied to the world he became sworn under. Not actually litrpg, harem. But well written.
https://www.amazon.com/John-Van-Stry/e/B004U7JY8I/
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Prax Venter - Entralled Series. A demon cat girl, a naga, and a construct join forces with the MC who is trapped in the game as AI's run rampant and take over the world. One AI takes a fancy to the MC and runs ...tests... on him to see how he will survive. Erotica with some litrpg elements.
https://www.amazon.com/Prax-Venter/e/B078L4SZ2V
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There's quite a bit of furry to be found in harem lit though:
Celestine Chronicles
https://www.amazon.com/Cebelius/e/B07DXD332M
Wild Wastes, Super Sales on Super Heros, and Otherlife
https://www.amazon.com/Randi-Darren/e/B06XQ1JM4W
https://www.amazon.com/William-D.-Arand/e/B01AY7PSG4/
I'd read them in this order: Otherlife (Omnibus), SSoSH (1-2), WW (Omnibus), SSoSH (3) -not out yet.
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Currently banned on Amazon because reasons:
Rescued: A Catgirl Harem Adventure by Jack Truxton. Yet another author caught up in the mass banning this summer. Hasn't bothered to return to Amazon. Might still be available somewhere else.
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Random Stuff:
David Aries - Half-Breed Hunter: Arrival
https://www.amazon.com/Half-Breed-Hunter-Arrival-David-Aries-ebook/dp/B07HB8HSY9
- kinda meh, but it has a cat girl and a dryad. not really monster girl, but its okay, but forgettable.
Maxx Whittaker - Temple of Cocidius - A monster girl harem Book 1 and 2.
Super short reads (63 pages). I have no opinions yet as I haven't started them, but its in the title?