A very unique way would be if they get trapped in a time - loop together. They have to rely on each other to break free and in the process, they learn things about each other that they never knew before, leading to a deep and different kind of relationship.
Their relationship could be developed through shared dreams. Since Naruto has the Kyuubi, it could cause some sort of spiritual connection between him and Sasuke where they start seeing each other's dreams. In these dreams, they could communicate and start to understand each other's fears and hopes better, which would then translate into their real - life relationship.
Their relationship could be developed uniquely by having Kakashi become a more emotional mentor to the female Naruto. Instead of his usual calm exterior, he shows vulnerability in front of her, which makes her see him in a new light. This could lead to a deeper level of trust and friendship between them.
Their relationship could develop uniquely if Naruto, influenced by the Kyuubi's instincts, starts to protect Sakura in a more primal way. For instance, he might sense danger towards her before she does, and his reactions are more animalistic. This makes Sakura see a different side of Naruto, and she begins to understand the depth of the connection between him and the Kyuubi.
Their relationship could start with mutual understanding. Naruto, who has always had a connection to the Kyuubi, now with a female form, could start to see her as more than just the beast inside him. They could have conversations about his dreams and her past.
Perhaps they could be brought together through a shared love for gardening. Naruto, who has always been interested in growing things (as seen with his love for ramen ingredients), and Mebuki, who might have a beautiful garden at home. They start sharing gardening tips and gradually open up to each other about their dreams and fears, thus deepening their relationship.
Maybe they are both involved in a competition within the village, like a ninja - skills tournament. At first, they are rivals, but as they face different opponents, they start to respect each other's abilities. This mutual respect then turns into a strong bond as they help each other train and improve.
Perhaps Hinata's Kitsune heritage comes with a set of rules and traditions. Naruto, in order to be with Hinata, has to learn and respect these. This process of him learning about her Kitsune side and adapting to it can create a very special and unique development in their relationship. He could participate in Kitsune festivals with her or learn the significance of Kitsune symbols which are important to her family.
A really unique way to develop their relationship is to have them swap abilities for a short period. Naruto gets some of Kurama's fox - like abilities and Kurama gets some of Naruto's human abilities. This forces them to understand each other's perspectives in a whole new way. They have to learn how to use these new abilities and in the process, they become closer. Another aspect could be that they are both transported to a parallel dimension where they are the only ones who know each other. They have to rely solely on each other to survive and find a way back home, which would greatly enhance their relationship.
One way is to put them in a situation where they have to take care of a young orphan together. This shared responsibility would force them to communicate, cooperate, and rely on each other. Through this, they would see different sides of each other. Sai might show his nurturing side, which Fem Naruto has never seen before, and she would show her motherly - like instincts. This would create a new level of closeness between them that is different from their normal ninja - comrade relationship.
Their relationship could develop uniquely if Sasuke, who is usually reserved, starts to open up to female Naruto in small, unexpected ways. For example, he could leave little notes for her around the house expressing his feelings, which is a big step for him considering his past. This could strengthen their bond as a couple and also show a different side of Sasuke to their children.