Perhaps she has inherited Snape's talent for potions and is trying to prove herself in Hogwarts while also dealing with the reputation her father has. She could be bullied because of Snape's cold exterior but then show her classmates her own unique charm and skills.
One idea could be exploring Snape's childhood before Hogwarts. Maybe he had a secret friendship with a Muggle that no one knew about. This could add depth to his character and explain some of his later actions.
One idea could be that Snape discovers Hermione has a rare magical ability that he's secretly been researching. He takes her on as an apprentice of sorts, much to the surprise of everyone. This could lead to a series of adventures where they explore the depths of this magic together and Snape slowly starts to see Hermione in a new light.
Well, a possible plot is her journey to discover her own identity outside of being Snape's daughter. She could be a talented witch in a different area than her father, like divination while he was into potions. And she might have to deal with people who either idolize or hate her father, which adds a lot of drama to her life.
A possible plot is that she has a special gift for potion - making, like Snape, but also a love for books and knowledge like Hermione. This leads her to create new potions based on old, forgotten spells she discovers in the library. However, there are those who are jealous of her abilities and try to stop her progress.
Another plot could be that Snape's daughter is enrolled at Hogwarts without anyone knowing her true identity. She has to navigate the school while hiding her relation to Snape. She might be sorted into Slytherin like her father and face challenges and prejudices from students who still view Snape as a dark figure. But as time passes, she shows them that she is her own person with her own values, while also honoring her father's memory.
One plot idea could be that Hermione gets angry at Snape for unfairly deducting points from Gryffindor. She confronts him in his office and they end up having a heated debate about fairness in the Hogwarts system. Another could be that Snape discovers Hermione is working on a dangerous magic experiment without proper authorization and she gets angry when he tries to stop her. A third idea is that Hermione overhears Snape making some snide remarks about her Muggle - born status and she angrily challenges his old - fashioned views.
One idea could be that Harry becomes a Defense Against the Dark Arts professor. He could teach students unique spells and techniques he learned from his own adventures. For example, he might introduce a class on how to combat dementors using the Patronus charm in more advanced ways. Another plot could involve Harry dealing with a student who has a connection to Voldemort, just as he did, and he has to guide the student to the right path. He could also face challenges from the school board who are skeptical of his teaching methods because of his unorthodox background.
One idea could be that the undercover professor has a secret mission to protect a special student. Maybe the student has a unique power or knowledge that dangerous forces are after. Another could be that the professor is actually from a rival academy, undercover to steal some important teaching methods.
One idea could be a story where a young trainer teams up with Professor Sycamore to research a new and mysterious Pokemon species that has been causing strange phenomena in the Kalos region. They embark on a journey filled with challenges and unexpected encounters.
One idea could be exploring Regulus Black's time as a professor and his relationships with students. Maybe he has a student who reminds him of his younger self, and he tries to guide them away from the dark path he once walked. Another could be a mystery where he has to solve a magical riddle in the school that is linked to his past secrets.