One plot idea could be that Crookshanks discovers a hidden passage in Hogwarts that leads to an ancient wizarding library. He then leads Hermione to it, and they find a powerful spellbook that helps them in their fight against the dark forces. Another could be that Crookshanks has a secret ability to communicate with other magical creatures in the Forbidden Forest and he enlists their help to save Harry from a dangerous situation. Maybe he can talk to the centaurs and they come to the rescue when Harry is surrounded by Death Eaters.
A more comical storyline could be Crookshanks accidentally getting into a magical mishap that gives him the ability to talk for a day. He then spends the day criticizing Ron's treatment of him, while also sharing some of the secrets he's learned from prowling around the Gryffindor common room at night. Hermione is both amused and exasperated as she tries to keep Crookshanks out of trouble.
Perhaps a fanfic where Lily Potter's spirit is able to communicate with Harry Potter during his difficult times at Hogwarts. She gives him advice and guidance that helps him through his struggles, like dealing with Snape's complex feelings towards him, or facing the challenges of the Triwizard Tournament. This would add an emotional and magical element to Harry's journey.
One idea could be exploring Bellatrix's backstory before she became a Death Eater. Maybe she had a complex relationship with her family that led her down the dark path. Another could be a story where she has a change of heart, perhaps due to an unexpected encounter with a character like Harry Potter. For example, she could see some of her own past self in Harry and start to question her loyalty to Voldemort.
Maybe a fanfic where the goblins of Gringotts go on strike. Since Harry has some influence with them due to his own vault and his adventures there, he gets involved in the negotiations. Along the way, he uncovers a plot by some Death Eaters who are trying to take advantage of the chaos to steal valuable magical artifacts from the bank. It would be a mix of politics, mystery and action.
A plot could be that the Harry Potter headphones are a creation of a young, brilliant wizard who is trying to revolutionize the way magic and Muggle technology interact. The headphones start to cause chaos in Hogwarts as they interfere with the existing magic there. Some students love them and think they're the coolest thing ever, while the teachers are worried about the potential misuse. Meanwhile, there's a mystery about the true power of the headphones that the main character has to figure out before they fall into the wrong hands.
A cool plot for a Harry Potter Twilight fanfic could be a competition. The wizards from Harry Potter and the vampires and werewolves from Twilight compete in a series of challenges. These challenges could test both magic and the unique abilities of the Twilight characters. Or perhaps a love triangle between a Harry Potter character, a Twilight vampire, and a Twilight werewolf. It would be interesting to see how the different cultures and powers interact in matters of the heart.
Another plot could focus on the lives of the secondary characters from the original series. For example, Neville could be the head of Herbology at Hogwarts and discovers a new, dangerous plant that has some sort of connection to an ancient magic. The 'carry on fanfic' could then be about how he and his students deal with it, with some cameos from the main characters.
One idea could be that a dragon escapes from Gringotts and Harry has to use his skills to track it down. Maybe the dragon has a special connection to a powerful dark magic item that Voldemort was after.
One idea could be that Voldemort somehow enters the Runescape world to seek more power. Harry and his friends follow him there to stop him. They have to learn the rules of Runescape quickly to be able to fight Voldemort. Another idea is that a Runescape wizard discovers a portal to the Harry Potter world and brings some of the unique items from Runescape, like special runes, which causes a stir in the wizarding world.
A great plot for a Harry Potter academy fanfic might be a time - travel scenario. A group of students accidentally travel back in time to the founding days of Hogwarts. They have to navigate the different rules and attitudes of that era while also trying not to change history too much. Or perhaps there's a plot where a student is wrongly accused of a major crime at the academy and has to prove their innocence. They'll need to use their wits and the help of their friends to find the real culprit.