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.
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.
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.
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.
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.
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.
There is a plotline where Harry trains in ancient magic. This ancient magic has been long forgotten by most wizards. He has to search for clues, study old texts, and train under the guidance of a reclusive wizard. This plotline is interesting as it explores a different aspect of the wizarding world's magic and Harry's role in uncovering and mastering it.
Maybe in this fanfiction, the fact that they are the Riddle Twins causes a stir in the wizarding community. Some people might fear them because of their connection to Voldemort, while others believe they could be the key to finally bringing true peace. Harry and Hermione then have to deal with the prejudice and the high expectations placed on them. They might have to prove that they are not like Voldemort and that their heritage can be used for good.
In some 'Harry and Hermione Heir of the Founders Fanfiction', a great plotline is their journey to understand the true intentions of the founders. As the heirs, they are expected to uphold certain values, but they need to figure out what those are first. They might travel to different places, meet old wizards or witches who knew the founders, and piece together the history. Along the way, they also deal with their own growing feelings for each other, adding a romantic sub - plot to the whole story.
In some fanfictions, there could be a plotline where Harry and Hermione start to realize their feelings for each other in a different way during their 6th year. They've been through so much together, and this year could be the turning point where their relationship evolves from just friendship. They might have more private moments, sharing their fears and hopes, and this newfound closeness could lead to a whole new dynamic in their relationship.