Well, perhaps in the fanfiction, the male Kyuubi can take on a human form temporarily. He and Naruto then enter a tournament in another village where they have to fight as a team. This would be interesting as they would have to learn to coordinate their attacks and defenses. And along the way, they could learn more about each other's personalities and grow closer as a result.
One idea could be that the male Kyuubi helps Naruto unlock a new form of power. Since the Kyuubi has its own unique chakra, it could blend with Naruto's in an unexpected way, leading to a new and powerful jutsu. Another plot could involve the male Kyuubi teaching Naruto about the history of the tailed beasts from his perspective. This could give Naruto a deeper understanding of his own situation as a Jinchuriki.