Well, you could start with the premise of Hermione being a transfer student to Jake's school in a modern - day setting. This would cause a stir as she tries to hide her magical abilities at first. But then, when strange things start to happen in the school, she has to use her magic to save the day. Along the way, she and Jake bond over their shared family connection and learn more about each other's worlds. Jake could introduce Hermione to modern technology, while she shows him the wonders of magic.
One idea could be a crossover in a magical - modern world setting. Maybe Hermione's magic causes some chaos in Jake's world. For example, her spells accidentally disrupt the technology in Jake's town. Another plot could involve them teaming up to solve a mystery that spans both their worlds, like a magical artifact that has ended up in Jake's modern world and is causing strange events.
In writing their relationship realistically, consider their personalities. Hermione is intelligent, studious, and used to a world of rules (in Hogwarts). Jake might be more laid - back. So, they could have some clashes in their approach to things. However, because they are siblings, they also have an unspoken loyalty. You can show this by having them defend each other. For instance, if Jake gets into trouble at school, Hermione could use her quick thinking and magic (discreetly) to get him out of it. And Jake could be there for Hermione when she misses her wizarding friends.
One idea could be that they discover their relation during a magical crisis. Maybe a dark force is threatening both the wizarding world and the demigod world, and their combined powers as siblings help save the day. For example, Hermione's magic and knowledge of spells combined with Percy's control over water and his demigod strength.
Some possible plot ideas include Hermione being mistaken for a powerful Grounder because of her magic. She could then use this to her advantage to broker peace between the different factions. Or maybe she discovers a magical element in The 100's world that she didn't expect, like a magical artifact left over from a pre - apocalyptic civilization. This could lead to a race among the different groups to obtain it, with Hermione in the middle trying to ensure it's used for good.
One idea could be that Hermione uses her intelligence to help Sam out of various tricky situations at school. For example, when Sam gets into trouble with a difficult teacher, Hermione devises a clever plan to get him out of it. Another plot could involve Hermione introducing Sam to the wizarding world, and Sam having to adjust to all the strange new things like magic spells and magical creatures. It could also be interesting if they team up to solve a mystery in their town that has both muggle and wizarding elements.
One plot idea could be that Hermione discovers she's Harry's sister early on. This changes their dynamic at Hogwarts. They might have a stronger bond and work even more closely together to fight Voldemort. Another idea is that Hermione's family has been hiding this fact from her all along, and she has to come to terms with her new identity while still dealing with the challenges of school.
The Asset from Shape of Water could be transported to Hellboy's world. There, it would be seen as a strange and new kind of creature. Hellboy would have to decide whether to help it find its way back or keep it safe in his world. This could lead to a series of adventures as they face different threats together.
One idea could be that a magical rift opens up between the Harry Potter universe and the Marvel universe where Hermione and Doctor Strange meet. They could team up to close the rift which is causing chaos in both worlds. Strange uses his magic to hold off the magical creatures spilling into the Marvel world while Hermione uses her vast knowledge of spells to find a way to close it from her side.
Well, perhaps Hermione is sent to the 'Vampire Diaries' world to retrieve a powerful magical artifact that has somehow ended up there. Along the way, she meets Damon and Stefan. She forms an unlikely friendship with them as they help her search for the artifact. In return, she uses her magic to protect them from some of the more dangerous supernatural threats in their world.
One idea could be that Hermione, with her vast knowledge from the wizarding world of Harry Potter, travels through time or a magical portal and meets Merlin. She could help Merlin with some of his more complex magical problems using her unique spells and techniques from Hogwarts. Another plot could involve them teaming up to defeat a common enemy that threatens both their worlds, perhaps a dark magic user who has found a way to bridge the two universes.
One plot idea could be that Hermione and Harry discover their twin connection early on. They might use their combined intelligence and magic to solve mysteries even faster at Hogwarts. For example, in dealing with the Philosopher's Stone mystery, they could come up with a more elaborate plan together to protect it from Voldemort. Another idea is that their bond affects the relationships with their friends. Ron might initially be a bit jealous of their closeness but then come to appreciate how their twin connection benefits the whole group.