I'm a Pet At Dali Temple (2018)

Both dramas are set in historical era with a romance-comedy genre about how the female or male lead are pets

Both are short dramas that start out light and fluffy then get more serious toward the end. The ML has a more sinister, darker personality trapped inside him that is trying to take control and who the FL is trying to save him from. Both FLs are from modern day and have traveled back to ancient times where they met the ML. Both FLs have some form of magic and are connected to the ML in a supernatural way. The ending is open but the two reunite in some way in modern day.

Both are fluffy and the ML has two completely different personalities.
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Both are typical time travel stories about a young female time traveller and her boyfriend in a fictional ancient kingdom.

Both are light shows with an animal lead (cat vs. bear).
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Very different in tone, but both have a ML who has a demon personality trapped inside him that is slowly taking him over. In both, most of the world wants to kill the ML to destroy the demon, but the FL is determined to save his human side.

Both are rather short and lighthearted historical drama from China. I watched I'm a Pet at Dali Temple first and watching Princess at Large reminded me of it and gave the same feeling.
Both dramas have female leads that travel back in time and both male leads have a medical condition that the female lead helps them with and throughout the drama they fall in love.
Also both were subbed by Lan Lan on FB.

Both dramas have the female lead travel to an ancient parallel universe. I think the vibes of the two dramas are also similar. The female leads also have a bubbly character (Though Xiao Tan is definitely more sassy) and the male leads are portrayed more cold on the outside but warm on the inside.

It's also about a cat turning into human and falling in love with their owner, just that in I'm a Pet At Dali Temple, the FL is the cat, while in Welcome, the ML is the cat.

One of the leads in both shows is some sort of animal. Both really cute plotlines but I'm a pet at Dali Temple is more serious that Semi Otoko.

In both dramas the ML has two personalities.
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In both the leading lady turns into a cat. Ru Xiao Lan is a young woman from the modern day. Through a series of circumstances, she travels to the ancient times as a cat. Purely by chance, she meets Qing Mo Yan who's suffering from a poison and as they kiss, they realize that they've found the solution to each other's complications. Deciding to stick together for their own gain, the two embark on a journey to find the five-colored stone that can break Xiao Lan's curse and the ghost grass that can cure Mo Yan's affliction.

Both are fluffy historical set dramas with a poisoned ML and a cutesy, upbeat FL who is from a different time or culture.

Both dramas have a modern day FL who time travels to the past and falls in love.
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Both have a Chinese historical fantasy dramas with king/prince who was poisoned and has a wife who can help get rid of it. Both have the same FL.