Well, in some fanfics, the Kyuubi's obsession might result in it influencing Naruto's chakra in a unique way. This could lead to Naruto developing new and unexpected jutsu. Also, the Kyuubi could be so obsessed that it tries to merge with Naruto in a different way than just lending its power, like actually becoming one entity with Naruto but still maintaining their individual consciousnesses to some extent.
Some fanfics may explore the idea that the Kyuubi's obsession is due to Naruto's unique spirit. So, it might start to manipulate events around Naruto to make him stronger faster. For example, it could draw out Naruto's enemies in a way that forces Naruto to quickly level up his skills. It could also be that the Kyuubi, out of its obsession, tries to change Naruto's view on the concept of power and how it should be used, which could lead to some really interesting moral and ethical dilemmas for Naruto.
One plot idea could be that the fem Kyuubi has a human form and she and Naruto have to go on a journey to find a way to restore balance in the ninja world that has been disrupted by some dark force. Along the way, they gradually fall in love as they face challenges together.
One idea could be exploring the relationship between Naruto and the Kyuubi no Kitsune in a more spiritual way. Maybe Naruto can have dreams where he actually communes with the fox spirit and gains new insights about his powers. Another plot could involve a situation where the Kyuubi's powers start to merge with Naruto in unexpected ways, causing him to develop new abilities that he has to learn to control quickly.
One idea could be that the female Kyuubi has the ability to transform into a human form and she becomes Naruto's secret protector. She uses her powers subtly to keep him out of harm's way while he's on his missions, and Naruto starts to notice strange things happening but doesn't know it's her at first.
The plot could involve the child being sought after by various ninja clans who want to use the power of the Kyuubi within the child for their own purposes. The child, with Naruto's teachings, resists and tries to find a way to use the power for the good of the village. Maybe the child discovers a new form of chakra control that combines Naruto's Uzumaki heritage and the Kyuubi's power.
The Kyuubi's obsession can accelerate Naruto's character growth. Since it's always around in some sense, Naruto may become more confident as he has this powerful being so interested in him. He might also become more aware of his own power potential.
One interesting plot idea could be exploring how Minato's relationship with the Kyuubi affects Naruto. For example, Naruto discovers some hidden memories of Minato's encounter with the Kyuubi that give him new powers or insights. Another idea is a story where Minato has to return from the afterlife briefly to help Naruto control the Kyuubi's power more effectively. Maybe there could also be a plot where the Kyuubi has a change of heart due to Naruto's kindness and decides to reveal secrets about Minato that no one else knew.
Maybe in the fanfic, Naruto gets injured while protecting the Fem Kyuubi from some other powerful force. This act of self - sacrifice makes her realize her deep love for him. Then, they start to train together, not just for power but also to strengthen their bond, sharing their secrets and fears during the process.
A really interesting plot could be that the Kyuubi bloodline in Naruto starts to have an effect on his relationships. Some people in the village might be afraid of him now that they know he has this powerful bloodline. On the other hand, some might see him as an even greater asset. Naruto then has to deal with the social implications while also training to control the new powers that come with his Kyuubi bloodline. He could also find out that there are other ninja out there with a similar bloodline from other tailed beasts, and they come together to form a unique group.
One idea could be that the power transfer is not straightforward. Maybe Kyuubi's power starts to change Naruto's appearance in unexpected ways, like giving him fox - like features that he has to learn to hide. This could lead to some comical and also tense moments as he tries to keep it a secret from his friends.
One popular plot idea could be Naruto gradually forming a bond with the fem Kyuubi. As he does so, he attracts a harem of characters who are intrigued by this unique relationship. For example, some might be drawn to his newfound power or the mystery around his connection with the Kyuubi. Another idea could be that the fem Kyuubi has to protect Naruto from those who would seek to use or harm him because of their relationship, and in the process, they both gain more allies that form the harem.