His backstory could be explored in more depth. We could see more details about his time after winning the Hunger Games and how it led to his state in the 75th Hunger Games. Maybe he had some untold experiences that made him more cynical or more determined, which would be different from what we know in the original series.
Haymitch's skills could be enhanced or presented in a new light. In fanfiction, he could have some hidden talents or abilities that were not fully shown in the original. For instance, he might be an even better strategist than we thought, or he could have some unique survival skills that he uses to his advantage during the 75th Hunger Games.
In some fanfictions, Johanna's loyalty to her friends, especially Haymitch, is made into a central part of her personality. She is shown as being extremely protective of him, which is a bit different from the books where their relationship was more complex. Haymitch in fanfiction may be more proactive in trying to change the system. In the original, he was more resigned to the Capitol's rule until Katniss came along. Here, he could be constantly looking for ways to undermine the Capitol, and Johanna could be his partner in this endeavor.
Haymitch is often characterized as a broken man in fanfiction. He has been through the Hunger Games as a victor and has seen the worst of it. He is usually depicted as cynical, sarcastic, and relying on alcohol to numb his pain. For example, he might make snide remarks about the Capitol's games. Effie, on the other hand, is characterized as proper and prim. She is very much into the Capitol's etiquette and appearance. She's always dressed up and concerned about presenting things in an orderly and proper way.
Well, in the original story, their relationship was mostly professional with a bit of underlying tension. In fanfiction, it could develop into a deep friendship right from the start. Maybe Effie starts to understand Haymitch's pain more quickly and they bond over their shared desire to protect the tributes. They could become confidants, sharing secrets about their pasts and fears.
In fanfiction, Cato might be developed as having a softer side. For example, towards Glimmer. In the original, he was mostly portrayed as a brutal and fierce competitor. But in fanfiction, he could show vulnerability when it comes to Glimmer, like caring about her safety more than just the victory. Glimmer could also be developed differently. Instead of just being a pretty face in the Games, she could be a strategic thinker, using her charm to manipulate not only the other tributes but also the Capitol audience.
Haymitch might start off as the typical cynical and jaded character we know from the original Hunger Games. But as the 50th Hunger Games progress, he could gradually develop a sense of hope. Maybe he meets a young tribute who reminds him of his own past self and he decides to mentor them more earnestly. This could lead to him becoming more selfless and brave.
She might be developed to be more of a rebel. In the original, she was quite innocent. But in fanfiction, she could take on a bolder role, maybe secretly training to fight against the Capitol.
In some fanfictions, Prim's character might be developed as more assertive than in the original story. Instead of being the innocent, sheltered girl, she becomes a strategic thinker. For example, she could be the one coming up with plans to outwit the other tributes.
One possible storyline could be Haymitch's internal struggle during the games. He might be haunted by his past experiences in the Hunger Games and be forced to relive some of his traumas. Another could be his strategic planning, how he uses his wits to outmaneuver the other tributes. Maybe he forms an unexpected alliance with a younger tribute and teaches them the ropes of survival.
In some 'James Potter alive' fanfictions, his character can be more mature. For example, if he comes back after a long time, he might have learned from his past mistakes. In the original, we saw him as a bit of a troublemaker in his youth. But in fanfics, he could be more responsible, especially if he realizes he has a second chance to be a better father to Harry or a better friend to his mates. He might also be more empathetic, having seen the consequences of his actions (or rather, his 'death') on those he left behind.
Often, fanfic authors give Cho a more complex backstory. Maybe she has family secrets related to the wizarding world's history. This can lead to her making different choices. For instance, she could be more involved in the Order of Phoenix's activities earlier on, rather than just being on the sidelines as in the original. This new backstory can also affect her relationships with other characters, like her friendship with Hermione or her rivalry with Ginny in a more nuanced way.