Power and control are common themes. Since the Kyuubi is a powerful entity, in the fem version, it's often about how she manages her power. Another theme is acceptance, as she is different in the Naruto world.
One interesting idea could be exploring how Naruto's relationship with the Kyuubi changes in a crossover scenario. Maybe in a different universe, they can communicate more freely and work together in unique ways.
One key element is how the Kyuubi's power is incorporated into the crossover. For example, if it's a Naruto - Dragon Ball crossover, will the Kyuubi's power be on par with Saiyan power? Another is the character interactions. If Naruto meets characters from another universe, how do they communicate and react to each other? Also, the plot should make sense in the context of both universes. If it's a Naruto - Harry Potter crossover, the magic and ninja techniques need to be integrated well.
Another theme is the exploration of a unique relationship. Since it's a crossover, the relationship between Naruto and the fem Kyuubi is different from the original Naruto - Kyuubi dynamic. It can range from a mentor - mentee type to a more equal partnership, and fanfics often explore how this relationship develops over time. There are also a lot of emotional exchanges, like trust - building and mutual understanding. For instance, in some stories, Naruto has to earn the fem Kyuubi's trust, and this process is full of challenges and revelations.
One important aspect is to focus on the character development. In Naruto, he has grown from an outcast to a hero. In a crossover fanfiction, you could show how he adapts to the new environment of Highschool DxD. Maybe he starts off being distrusted by the devils and angels because of his unknown power source (the Kyuubi). Then, as he shows his true nature, they start to accept him. Another point is the plot. You could create a conflict that involves both the threats from the Naruto world (like rogue ninja or Akatsuki members) coming into the Highschool DxD world and the internal conflicts within the Highschool DxD world itself, such as power struggles between the different factions. This would keep the story exciting and full of action.
Obviously Naruto and the Kyuubi are the main focuses. Since it's about their crossover, the story often revolves around their connection and how they interact with the new elements introduced in the crossover.
Well, 'Naruto: The Crossover with One Piece' is a cool fanfiction in this regard. It has Naruto meeting Luffy and his crew and the adventures they go on together are quite exciting. Some fanfictions like 'Kyuubi's Power in a New Realm' explore how the Kyuubi's power would be perceived and used in a different fictional world. And 'Naruto's Multiverse Crossover' is a really fun read as it throws Naruto into multiple crossovers with different universes.
The plot might involve a threat that endangers both Naruto's world and the world of Rosario Vampire. Naruto, with his Kyuubi - enhanced abilities, teams up with the vampires and other creatures in Rosario Vampire. They'd have to combine their different powers, like Naruto's Rasengan and the vampires' super strength, to fight against the common enemy. It would be a wild mix of ninja action and vampire drama.
Naruto would probably be very curious about the vampires and other creatures in Rosario Vampire. He'd be his usual friendly self, trying to make friends. The vampires might be initially wary of him, especially with the Kyuubi's power, but his positive attitude could win them over. Tsukune, from Rosario Vampire, could learn a lot from Naruto about determination and fighting spirit.
The Kyuubi within Naruto represents a powerful and often uncontrollable force. In a crossover with the Justice League, this could be a source of both conflict and cooperation. The League might be wary of the Kyuubi's power, but Naruto's willpower to control it could earn their respect. They could work together to fight a common enemy that is drawn to the unique power that Naruto and the Kyuubi possess. Maybe an alien threat that wants to harness the Kyuubi's chakra for its own evil purposes. Naruto could use his Rasengan and other jutsu in combination with the League's powers, like Superman's strength or Batman's strategic mind, to defeat this enemy.