Perhaps she discovers a different magical school or a secret magical community outside of the Hogwarts system. In this fanfiction, she could be mentored by an eccentric and powerful wizard who has his own way of teaching magic, far removed from the traditional Hogwarts curriculum.
Another plot could be that Hermione, without going to Hogwarts, becomes involved in the Muggle world's study of magic in a more in - depth way. She might try to bridge the gap between the Muggle understanding of the occult and the wizarding world's magic. She could use her vast knowledge from Muggle studies to explore magic from a different perspective, leading to new magical discoveries that Hogwarts might not have considered.
One possibility is that Harry grows up in the Muggle world completely unaware of his wizarding heritage. He might lead a normal life, going to a regular school, making Muggle friends, and having no idea about the magical world that could have been his. Maybe he has a natural aptitude for something like martial arts or a particular academic subject that in the wizarding world would be replaced by magic.
One possibility could be that Snape grows up in a different magical environment, perhaps in a small, hidden magical community that has its own unique way of teaching magic. He might develop his skills in potion - making and the Dark Arts in a more self - taught or community - guided way. Without the influence of Hogwarts, his relationships would be very different. He may not have the same intense rivalries or unrequited love for Lily Potter.
One possible plot could be that Harry Potter discovers a different magical school. Maybe he stumbles upon a hidden school in the Muggle world that has been secretly teaching magic. He could form new friendships and face different types of magical challenges there. It would be a completely new magical experience for him, away from the familiar Hogwarts environment.
Her relationships would be different. Instead of having school friends like Harry and Ron, she might form alliances with other self - taught wizards or those from different magical backgrounds. This could lead to a more diverse and complex social network, which in turn would shape her character in unique ways. For instance, she could become more diplomatic as she deals with different magical cultures outside of the Hogwarts - centric wizarding world.
The Dumbledore character could still be important. He might be secretly watching over Harry, guiding him from a distance. Another character could be a new wizard or witch that Harry meets in the Muggle world who has a special mission related to Harry. For example, a young witch who has been exiled from the wizarding world but has the knowledge to help Harry understand his powers. And of course, Voldemort would still be a main antagonist as his threat looms over the entire wizarding world whether Harry is at Hogwarts or not.
Well, it could be that Hermione inherits Hogwarts due to some magical law or prophecy. She then uses her intelligence and knowledge to make all kinds of reforms, like improving the curriculum for all students.
Well, perhaps the plot could involve Hermione discovering some ancient secrets of Hogwarts that are only known to the heir. Maybe she has to face challenges that test her intelligence and magic skills in a whole new way.
Maybe she'd take control to better protect the students. She might enforce stricter security measures around the castle and grounds. Hermione is known for her caution and strategic thinking, so she could organize the defense of Hogwarts in a more efficient way against potential threats, like Death Eaters or other dark forces.
Perhaps the story could revolve around them facing challenges within the Hogwarts faculty. There could be some old - fashioned professors who oppose their modern teaching methods. Harry and Hermione then have to prove that their ways are beneficial for the students. They might also discover new magical abilities in some of the students that were previously overlooked, and help those students develop their skills.
One possible plot could be that they meet in a muggle library. Hermione is there researching magic in the guise of general knowledge books, and Harry stumbles upon her while looking for a quiet place to escape from the Dursleys. They start chatting about books, and Hermione is intrigued by Harry's strange yet endearing manner. They then realize they both have a connection to the magical world.