Well, you can try searching on fanfic platforms like Archive of Our Own. Look for tags related to 'kaneki x kaneki' and exclude any tags that might indicate lemon or adult content. There might be some great platonic or friendship - centered fanfics about these two characters.
One challenge could be the difference in their personalities. Haise is more reserved and Mutsuki can be quite intense. This could lead to conflicts within their partnership, like misunderstandings during missions. Another challenge might be their loyalty to the CCG. If they start to question the CCG's motives, they would have to decide whether to stay loyal or follow their own moral compass. For example, if the CCG orders them to do something unethical.
A common theme is the exploration of their dual identities. Given that they are the same character in different states, fanfics might delve into how they interact with this shared yet distinct self - awareness. Another theme could be self - discovery, as they come to terms with who they are both individually and in relation to each other.
One possible scenario in a Naruto - Kaneki fanfiction could be that Kaneki somehow ends up in the Naruto world. Maybe through a strange portal or some sort of jutsu gone wrong. He might initially struggle to adapt to the different environment and the presence of chakra. But his own unique kagune abilities could be seen as a strange new form of power in the Naruto universe.
Unfortunately, Kaneki did die in the manga. This event was a turning point that brought about many changes in the storyline and the dynamics among the characters.