If you're looking for manga similar to I'm a Behemoth, an S-Ranked Monster, but Mistaken for a Cat, I Live as an Elf Girl's Pet, you might like these titles.
Reincarnated as a sentient weapon with memories of his past life, but not his name, a magical sword saves a young beastgirl from a life of slavery. Fran, the cat-eared girl, becomes his wielder, and wants only to grow stronger, while the sword wants to know why he is here. Together, the strange duo’s journey has only just begun!
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Both MC's are reincarnated as non humanoids, are really strong and are taken care of by a girl who cherishes them. It also as the same type of background, skills, adventuring, guilds, monsters
After being worked quite literally to death, corporate slave Routa Okami's dying wish is to be reborn as the well-loved pet of a rich family. When a compassionate goddess actually grants him his wish, Routa commits himself to the lazy, carefree, all-you-can-nap lifestyle of a pampered pup--complete with a beautiful owner and all the delicious food he can eat! But as Routa grows...and grows...and grows...he realizes something is terribly wrong. With his enormous body, razor-sharp teeth, and fierce visage, it's painfully obvious that he was reincarnated not as a dog but as a giant wolf. And not just any wolf--the legendary wolf king Fenrir!
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Both feature MC's that live as pets despite being super strong, and both of their ownerd are completely oblivious. Very similar concept for both of them.
Paw pads wrapped in white fur. Fluffiness around the neck. A bushy tail. A rounded figure that was the very definition of fur ball! ――A certain Japanese girl had been reincarnated into such a fox cub; Milfiria. Milfiria was told to watch the house by her mother, as the mother left for the capital. However, unable to bear with the loneliness and deciding to chase her mother to the capital, Milfiria became lost in a fort protected by strong knights.
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They both have small four legged animal characters that integrate themselves into a society with a bunch of chill breathing room however the behemoth one is more vulgar meanwhile Kita no Toride Nite is more slice of life with a slow wind up to what I will assume in the future will lead to some combat.
42 year old "shachiku" (company slave) Matsuda Takeshi gets worked to death, as is customary in Japan. His one dying wish is to work for a decent enterprise, not the black company he had been working for. His wish is heard by a god who, for his own amusement, has him reincarnate as a young elf male in another world, with increased affinity for earth magic and ability to command golems. The new golem master sets out on a quest to acquire the Seven Treasures left behind by a legendary mage from 1000 years ago.
As his casket was being closed, The Great Sage Marlin Endlight used his infinite wisdom to reincarnate himself into a "Endlessly Evolving Slime". He decides to enjoy his new slimey life, until his third daughter finds him and casts a taming spell on him! Living as a familiar to his foster daughter isn't too bad: Not only is he constantly getting hugs, but he can stealthily continue to evolve and watch over all his beloved daughters. Until he obtains a human form, he will hide his true identity from them. But let it be known that while Sura-chan (ex-Great Sage) is around, no number of greedy fake researchers, bandits or evil cults will harm his girls!
Naoe-kun, a massage therapist, is about to head home for the day when he’s saddled with a rather strange patient. This lovely lady has emerald eyes, pointy ears, and grew up in the forest–everything about her screams “elf,” except for one thing: her bodacious body. It turns out she left her world but loves junk food in this one, and now her obsession has caught up with her. Can Naoe-kun help this lovable elf girl lose the weight–and keep it off?
Naoe-kun, a massage therapist, is about to head home for the day when he's saddled with a rather strange patient. This lovely lady has emerald eyes, pointy ears, and grew up in the forest–everything about her screams “elf,” except for one thing: her bodacious body. It turns out she left her world but loves junk food in this one, and now her obsession has caught up with her. Can Naoe-kun help this loveable elf girl lose the weight–and keep it off?