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.
Dumbledore could also make an appearance. He often has his eye on the students and might offer some wisdom or assistance to the character who is trying to do Hermione a good deed. He could be the one who gives a hint about how to help Hermione in a particular situation.
Well, one possible plot could be Ash and Misty teaming up to save a group of Pokémon from a powerful villain in a very unique way. Another could be them exploring a mysterious new region together and discovering rare Pokémon. Or perhaps they have to overcome some personal differences to become better friends and Pokémon trainers.
Well, one possible interesting plot could be Hermione using her intelligence in a mercenary role to outwit her opponents. For example, she might use her knowledge of magic to create unique battle strategies.
One possible plot could be Hermione using her intelligence to find a way to repel Dementors without using a Patronus. Maybe she discovers some ancient magic or potion that can keep Dementors at bay. Another plot could involve a Dementor being somehow controlled by a dark wizard to specifically target Hermione, and she has to outwit both the Dementor and the wizard. There could also be a story where Hermione befriends a Dementor in a very strange turn of events, perhaps by understanding its true nature and finding a way to communicate with it, which would be a very unique take on the relationship between a character and a Dementor in fanfiction.
First, really study Hermione's character. Read the original books to understand her traits like her intelligence, determination, and loyalty. Then, come up with an interesting plot. It could be a new adventure at Hogwarts, or a different take on an existing story arc. For example, what if Hermione discovered a new spell and had to keep it a secret? Also, make sure your writing style is engaging. Use vivid descriptions to bring the wizarding world to life.
One possible plot could be that Peter Parker discovers ballet as a form of unique training for his superhero agility. He might start taking ballet classes secretly, and then his friends in the superhero world find out and are initially confused but later impressed by how it enhances his combat skills.
Perhaps in the fanfiction, Hermione gets even with those who underestimated her. She could expose their wrongdoings or secrets, using her skills in research and deduction. For example, if someone tried to take credit for her work, she'd find a way to prove it was hers and make them look foolish in the process.
Another possible plot is that Hermione, as the heir of Merlin, is prophesied to bring about a new era of magic. However, there are those in the wizarding world who oppose this change. So she has to gather allies, including some unexpected ones, and fight against the old - fashioned and conservative forces that want to keep the status quo. Along the way, she also has to deal with her studies at Hogwarts and her relationships with her friends like Harry and Ron.
In a fanfiction plot, it could be that Hermione discovers a new spell that requires a unique form of casting with the fingers. Draco, being knowledgeable about some dark magic that has similarities, tries to help her. Their fingers work in tandem during the spell - casting practice, and this creates an unexpected connection between them. This connection then grows into a friendship that has to overcome the prejudices of their past. For example, Hermione has to deal with the fact that Draco was once a Death Eater supporter, and Draco has to accept Hermione's Muggle - born status in a more positive light.
One interesting plot could be Hermione and Draco forced to work together on a project for the wizarding community. As they spend time together, they start to see each other in a new light and gradually develop feelings. Their families initially oppose the relationship due to their past rivalries at Hogwarts. But through various challenges and misunderstandings, they manage to form a family of their own, with Hermione's intelligence and Draco's family influence creating a unique dynamic.