One plot idea could be Naruto and Kurama going on a journey outside the Hidden Leaf Village together. They face various challenges like dealing with rogue ninjas or strange beasts. Along the way, they learn more about each other's pasts and grow even closer as friends.
One idea could be that Naruto and Kurama have a day - out in the Hidden Leaf Village. They visit all the places Naruto used to go as a kid, like Ichiraku Ramen, and Kurama makes funny comments about human food. Another could be that they team up to prank the other villagers in a harmless way, just for fun.
One idea could be a fanfic where Kurama and Naruto have a telepathic adventure outside of the normal Naruto world. They explore different dimensions and encounter strange creatures together.
One interesting plot could be that Kurama has a hidden past related to the creation of the ninja world. As Naruto and Kurama become friends, Kurama reveals this past. It could involve ancient ninja clans and forgotten jutsus. Naruto then uses this knowledge, along with Kurama's power, to bring about a new era of peace in the ninja world.
One plot idea could be Kurama teaching Naruto some ancient and powerful jutsu that only he knows. Since Kurama has a vast knowledge of chakra and ninja techniques from long ago, he could pass on this knowledge to Naruto in a unique way, like through dreams or during their mental conversations.
One plot idea could be Naruto and male Kurama having to team up to face a new and powerful enemy that neither could defeat alone. They start to understand each other's powers and personalities better during the battle. Another could be Kurama teaching Naruto a new and unique form of chakra control that is exclusive to the nine - tailed fox. Or perhaps they go on a journey to discover the origin of Kurama's power and along the way, they form a deeper bond as friends.
A really interesting plot might be that Kurama decides he wants to experience the human world more like Naruto does. So Naruto takes him on a 'tour' of the Hidden Leaf Village, showing him all the things he loves about it. But during this time, they notice some strange things going on in the village that seem to be related to an old enemy of Kurama's. They then have to use their partnership to figure out what's going on and stop it before it's too late. This could involve them using their unique bond to communicate with the villagers in a new way and uncover secrets that have been hidden for years.
A plot could involve Naruto having to go on a journey within his own mind to save Kurama from some sort of dark influence. During this journey, they discover hidden aspects of each other's personalities. Naruto might find out that Kurama has a soft side that he's never shown before, and Kurama could learn about Naruto's insecurities. This could lead to a stronger bond between them, and when they return to the real world, their combined strength is even greater. And as their relationship deepens, they face challenges from the outside world that test their new - found connection.
Perhaps in the fanfiction, the female Kurama forms a special bond with Naruto where she can transfer some of her unique powers to him in a different way than in the original story. This could lead to Naruto developing new jutsu and facing new enemies that are attracted by this new power. For example, a group of rogue ninjas who want to steal this power-transferring ability.
One idea could be that Yakumo Kurama's unique powers somehow become linked to Naruto's Nine - Tails chakra, creating a new and powerful combination. They could then face a common enemy together that neither could defeat alone.
One idea could be that the Kurama brothers have a secret mission to protect Naruto from an ancient evil that only they know about. They use their unique powers and knowledge to train Naruto in ways that no one else can.