One possible plotline could be that Harry hypnotizes Hermione to help her overcome her fear of a particular spell. For example, the Patronus charm. Under hypnosis, she is able to face her inner demons related to the spell and eventually masters it. Another plotline might be that Harry hypnotizes Hermione as part of a prank gone wrong. But then they end up learning something new about each other's subconscious minds. A third plotline could be that Hermione asks Harry to hypnotize her to retrieve a lost memory, which leads to a whole adventure of discovery in her past.
Well, in some fanfictions, Harry hypnotizes Hermione to make her more confident. Maybe she has to give a big speech in front of the whole school and is really nervous. The hypnosis gives her the boost she needs. Also, it could be that Harry hypnotizes Hermione to unlock a hidden magical ability. This ability could be something that has been dormant within her for a long time. And then there's the idea that Harry hypnotizes Hermione because he thinks she's been acting strangely due to a spell cast on her, and through hypnosis, he tries to find out what's really going on.
Some fanfictions explore a different relationship dynamic between them. Maybe Harry has a problem that only Hermione can understand and help him with, and this brings them closer in a way that's different from their normal friendship. It could be something related to his connection with Voldemort or his family history.
In some fanfictions, their training might involve time - traveling. Maybe they go back in time to learn from the founders of Hogwarts. Harry could learn how to better control his connection to Voldemort through this time - traveling training, and Hermione could study ancient magic from the founders. This would add a whole new dimension to their skills and knowledge.
One possible plotline could be Hermione using her intelligence to create a stable and loving home environment for Harry. Maybe she helps him deal with his PTSD from his past traumas. Another could be them facing magical threats together as a family, with Hermione teaching Harry new spells and ways to protect himself.
One interesting plotline could be Harry and Hermione discovering a long - lost secret vault in Gringotts. Maybe it contains powerful magical artifacts that can change the course of the wizarding war. Another could be that they are on a mission to retrieve something from the vault that is crucial for their fight against Voldemort, like a spellbook with ancient and powerful spells.
One possible plotline could be that they are practicing magic for an upcoming difficult exam at Hogwarts. They might be working on advanced spells like the Patronus charm and Hermione is helping Harry perfect it.
One possible plotline could be that they escape from a dark wizard's lair. Maybe they use their combined magic skills and Hermione's extensive knowledge to find a secret passage out. Another could be escaping from a dangerous magical creature's territory by using clever spells and potions.
Perhaps a plot where they all become animagi and have to use their animal forms to solve a mystery in the Forbidden Forest. Draco as a sleek snake, Harry as a stag, and Hermione as an otter, they must navigate the forest's dangers and uncover the truth about a strange magical disturbance.
A third plotline could revolve around a magical object or a special power that only Harry seems to have access to. For example, if there was a new magical amulet discovered that has a special connection with Harry. Hermione, being the knowledge - thirsty witch she is, might be jealous that Harry gets to experience and explore the powers of this amulet while she is left out. This could lead to a rift in their friendship until they figure out how to share or include Hermione in the discovery.
One interesting plotline could be them trying to keep their relationship a secret from their friends at first. Since they are both very close to Ron, they might worry about how he'll react. Another plotline could involve them using their combined intelligence to solve a new mystery at Hogwarts that no one else has been able to figure out. For example, a strange magical occurrence in the Forbidden Forest that seems to be related to an ancient spell.
A plotline could involve them discovering new magical abilities or powers as a result of this trauma. It's possible that the emotional upheaval of being disowned unlocks latent magic within them. They could then use these new powers to not only better their own situation but also to help other outcasts in the wizarding world. Maybe they start a secret group for those who have been rejected by their families.