Well, Harry Potter would most likely be one of the main characters. He is Hermione's close friend and they often face challenges together in the original series, so it's reasonable to assume he'd play an important role in the fanfic as well.
One interesting plot twist could be that Hermione discovers a hidden spell within the Goblet of Fire that no one else knew about. This spell could change the nature of the Triwizard Tournament in unexpected ways.
Often, you'll see original characters who are students from other schools. For example, there might be a really smart and mysterious student from Durmstrang who becomes friends or rivals with Hermione. They could have their own motives for being at Hogwarts during the Goblet of Fire events.
One interesting plot twist could be that Hermione is secretly entered into the Triwizard Tournament not by the Goblet, but by a dark wizard who wants to use her as a pawn. This would put her in a very dangerous situation right from the start.
One great fanfic could be about Harry and Hermione getting unexpected advice from McGonagall regarding the Goblet of Fire. Maybe McGonagall suspects some foul play early on and warns them to stay away from it, but their curiosity gets the better of them.
One interesting fanfic could be where Harry and Hermione team up to solve the mysteries behind the Goblet of Fire in a more in - depth way than in the original book. Maybe they discover a hidden plot early on and work together to expose it.
One fanfic that comes to mind is 'Hermione's Unforeseen Adventure in the Goblet of Fire'. In this fanfic, Hermione accidentally switches places with one of the champions in a magical mishap. She has to then compete in the tasks while trying to figure out how to reverse the spell. It's a really unique take on the Goblet of Fire story.
One interesting Hermione in Goblet of Fire fanfic could be one where she has to solve a mystery related to the Triwizard Tournament that the original story didn't cover. For example, she might discover a hidden plot by a group of dark wizards who are trying to manipulate the tournament for their own evil purposes. Another could be a fanfic that focuses on Hermione's relationship with other characters during that time, like a deeper friendship with Cedric Diggory. She could be helping Cedric prepare for the tasks in ways that the books didn't show.
Yes, it can be a somewhat common theme. In fanfiction, writers often explore different relationship dynamics that weren't fully developed in the original 'Goblet of Fire' story. Some fans might be intrigued by the idea of Hermione and Harry having a more romantic connection, so they write about Hermione kissing Harry to create new and interesting storylines.
One common theme is friendship deepening into something more. In many fanfictions, the events of the Goblet of Fire bring Harry and Hermione closer together in a way that makes them realize their feelings for each other go beyond just friendship. Another theme is the exploration of the magical elements. Since the Goblet of Fire is full of magic, fanfictions often expand on the magic in unique ways, like new spells or hidden magical artifacts related to the tournament.