The relationship could develop uniquely if the OC is an artist. The OC could see Yuki as a muse and start drawing him. Yuki, who is not used to being the center of someone's creative attention, becomes curious about the OC. This mutual interest in art and the OC's view of Yuki as more than just a student or a zodiac member can lead to a deep and different kind of relationship.
If the OC is a bit of a rebel. They introduce Yuki to things he has never done before, like sneaking out at night to go to a local music concert. Yuki, who has always followed the rules, starts to enjoy this new sense of freedom with the OC. This shared experience of breaking out of their comfort zones can make their relationship develop in a very special and unexpected way.
You can also develop your OC's personality based on their hobbies and interests. If they love gardening, they could be a calming presence, like Tohru in some ways. But they might also be a bit stubborn when it comes to their plants. Also, think about how they interact with the existing Fruits Basket characters. Do they get along well with Kyo right away, or do they have some initial clashes? Their relationship with the characters can further define their uniqueness.
Fanfictions often change their relationship dynamics by exploring different emotional aspects. For example, in some, Kyo might show more vulnerability towards Yuki, which is a big shift from their initial rivalry. This can lead to Yuki being more empathetic towards Kyo. Another way is by changing the power balance. In the original, they had a certain power dynamic, but in fanfiction, it could be reversed, like Yuki being the one to physically protect Kyo instead of the other way around.
One plot idea could be that the OC is a new student at the school Yuki attends. They accidentally bump into each other in the hallway, and Yuki's polite apology makes the OC intrigued. As the story progresses, the OC discovers Yuki's secret about being a part of the Sohma family and helps him come to terms with his insecurities regarding his place in the family and among his peers.
Their relationship could develop uniquely through shared dreams. Maybe they start having the same nightmares about an upcoming apocalypse, and they have to figure out what it means together. This shared experience could bring them closer as they rely on each other's interpretations of the dreams.
The relationship could develop through music. If the OC plays an instrument or loves music, Italy could introduce them to Italian opera and folk music. They could attend music festivals together and this shared passion could bring them closer.
In many such fanfictions, Yuki's friends would likely launch a desperate search to find him. Kyo might put aside his differences with Yuki in order to rescue him. They would follow any leads, no matter how small. For example, if there was a witness who saw the kidnapper's vehicle, they would track it down. And Tohru would be a source of emotional support for everyone involved, constantly worried about Yuki's safety and trying to keep everyone's spirits up during the search.
Kyo could develop by becoming more confident in his human form. He might start to see himself as more than just the cat that is shunned in the Sohma family. With Tohru's influence, he could learn to accept himself fully.
The relationship could be developed through shared secrets. For instance, the OC could have a secret past related to a meta - human experiment that they don't want anyone to know. Barry discovers this secret and instead of judging, he helps the OC come to terms with it. This mutual trust and understanding can deepen their relationship. Another way is if the OC has a special interest or hobby, like painting portraits of Central City's heroes. Barry could be the subject of one of these portraits, and through this, they start to have deeper conversations about their hopes and fears.
It could be a jealous rival from school. Maybe someone who's envious of Yuki's popularity and good looks. This person might have snapped and decided to kidnap Yuki to teach him a lesson.
In Kyo x Yuki fanfiction, 'character growth through each other' is a popular trope. They can learn from each other's strengths and weaknesses. For example, Yuki can learn from Kyo's more straightforward and passionate nature, while Kyo can learn from Yuki's calm and collected demeanor. 'Mutual understanding' is also a big one. As they start to understand each other better, they form a deeper bond. Additionally, the 'sacrifice for each other' trope can be seen. They might be willing to put themselves in harm's way to protect the other, which shows the depth of their relationship in these fan - created stories.