One possible interesting plot could be helping Hermione with her overloaded study schedule. Maybe the protagonist takes on some of her research tasks in the library, which leads to them uncovering a long - lost magical secret together.
Hermione is central, of course. The other main character could be a new student who has a special skill or power. For example, this new student might be able to communicate with magical creatures in a unique way. When Hermione is having trouble with a magical creature - related project, this student steps in to do her a favor. There may also be a strict teacher character who initially opposes the favor - doing but then comes around as the story progresses.
One possible plot could be helping Hermione with her overloaded study schedule. Maybe the protagonist offers to take on some of her library research tasks so she can have a bit of a break.
Maybe Hermione was trying to organize a study group for the upcoming exams but was having trouble getting everyone together. You stepped in and used your social skills to gather all the students she wanted. As a result, the study group was a great success and Hermione was very appreciative.
Well, in the Triwizard Tournament, Hermione was involved in helping Harry prepare. But she also had her own studies to keep up with. You offered to take over some of her note - taking duties for the classes she missed while helping Harry. This way, she didn't fall behind in her academics and could fully support Harry in the tournament. She was really touched by your kindness.
One possible interesting plot could be Hermione using her vast knowledge to teach unique and magical parenting techniques in the class. For example, she might introduce spells to soothe fussy babies that are specific to the wizarding world.
One interesting plot could be a time - travel scenario. Hermione somehow travels back in time to Tom Riddle's Hogwarts days. She tries to prevent him from becoming Voldemort. Maybe she uses her knowledge of magic and the future to show him a different path, like introducing him to the power of love and friendship that he was deprived of as a child.
Well, a possible plot is that Hermione discovers a hidden diary of Tom Riddle that has some sort of magic she has never seen before. As she delves into it, she somehow gets connected to Tom's memories and experiences his past. This could lead to her trying to understand what made him turn out the way he did and she might attempt to change his future. Another plot could be that in an alternate universe, Tom Riddle didn't become evil and he and Hermione meet at Hogwarts as normal students. They end up competing in academics and gradually develop a strange sort of friendship that challenges both of their beliefs.
In some fanfics, their fight might be triggered by a misunderstanding about their future careers. For example, Hermione might think Ron doesn't support her ambition to further her studies in magic, while Ron may feel Hermione is being too pushy about his own choices.
One interesting plot could be them facing magical challenges together from a young age. Since they are raised together, they might have a unique bond that helps them solve puzzles and overcome dark forces more easily. For example, they could encounter a mysterious magical creature in their backyard and figure out how to deal with it using their combined knowledge and skills.
In some 'Harry and Hermione get married fanfic', they might have to deal with a new dark threat that emerges right after their wedding. This threat could be related to a long - lost dark magic artifact that the villains want to use to take over the wizarding world. Harry and Hermione, being the intelligent and powerful couple they are, use their wits and magic to fight against this new evil. They might even get help from some unexpected allies from different houses in Hogwarts.