Well, the werewolves in Harry Potter, like Remus Lupin, are more about the monthly transformation and the struggle with their inner beast within the context of the wizarding world. In Twilight, werewolves are more of a tribe - based, shape - shifting species. In fanfiction, you could blend these by having a character from the Harry Potter world exposed to the Twilight werewolf 'culture' and learning new ways to control their transformation. For example, they might learn some sort of spiritual or tribal method that helps them better deal with their werewolf side.
One idea could be a story where a character from the Harry Potter world, perhaps a student at Hogwarts, discovers they have a connection to the werewolves in Twilight. Maybe they are bitten during a magical accident and start to show traits of both a wizard - with their magic - and a Twilight - style werewolf. This could lead to all sorts of interesting plotlines as they try to hide their new identity from both the wizarding world and any vampires or werewolves in the Twilight realm.
The idea of the outsider is present in both. Belle was an outsider in her village, and Harry was an outsider in the wizarding world at first. In a fanfiction, a new character could be introduced who is an outsider in both the Beauty and the Beast world and the Harry Potter world. This character could be the link between the two stories, trying to find their place and in the process, bringing the two worlds closer together.
The idea of fate is present in both. In Harry Potter, there are prophecies that seem to guide Harry's destiny. In The Princess Bride, the idea of true love's path is like a form of fate. Fanfiction could play with this idea. For example, a prophecy in the combined world could predict that only by the union of the magic of Harry Potter's world and the courage of The Princess Bride's characters can a great evil be defeated. This would bring the two universes together in a more fateful way.
The power of friendship is a strong theme in Harry Potter. In Guilty Crown, the relationships between characters also play a crucial role. A fanfiction could blend these by having the friendships in Harry Potter help strengthen the bonds between characters in Guilty Crown during a difficult time. For example, Hermione's intelligence and loyalty could help the characters in Guilty Crown come up with better strategies.
The theme of sacrifice is present in both. In Harry Potter, Harry sacrifices himself to save the wizarding world. In Ender's Game, Ender sacrifices his childhood for the sake of humanity. In fanfiction, this could be explored further. Maybe a character from Harry Potter has to sacrifice something in the Ender's Game universe to achieve a greater good. The theme of friendship is also key. Harry has Ron and Hermione, and Ender has his friends at Battle School. Fanfiction could show how these different friendship dynamics interact when the two worlds meet.
One of the main themes is acceptance. Werewolves in the Harry Potter universe often face discrimination, and fanfictions usually explore how they strive for acceptance from the wizarding society. For example, stories might show werewolves trying to prove that they can control their condition during full moons.
One way is through character creation. For example, a new character could be based on a Norse god or goddess, with their powers and personalities reflected in the Harry Potter world. So, like a character inspired by Thor could have the power of lightning in the magical context of Hogwarts.
The worlds can be blended by having Barbie visit Diagon Alley. She could be amazed by all the magical items and use her fashion sense to customize her wizarding robes. For instance, adding some sparkly elements that are typical of Barbie's style.
The blend can occur through the use of magic in relation to trigonometry in solving problems. For example, in a fanfiction, a magical creature is lost in a forest that is magically generated with trigonometric patterns. The characters need to use their knowledge of both magic and trigonometry to find the creature. Also, a character's magical power could be related to their understanding of trigonometry, so as they learn more math, their magic becomes stronger and more versatile.
The themes could be blended by having a common enemy in the form of Medusa. In Harry Potter, there are dark forces that the characters fight against, and in Tokyo Ghoul, there are the conflicts between ghouls and humans. Medusa could be the overarching threat that unites both worlds. Her power to turn things to stone could be a metaphor for the rigidity and destruction in both worlds. For example, in Tokyo Ghoul, the constant struggle between the two species is causing a kind of'stagnation' in society, similar to being turned to stone.