One idea could be that Haymitch and Effie have to team up to secretly protect Katniss and Peeta in a different way than in the original story. Maybe they discover a plot within the Capitol that endangers the tributes and they have to work together to stop it without getting caught.
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.
To some extent, it is. The story of Effie Grey takes inspiration from actual historical circumstances and figures, but it might have some fictionalized elements for dramatic effect.
Effie's story in Dream Girls is quite complex and full of challenges. She goes through various ups and downs as she pursues her dreams in the entertainment industry.
One interesting plotline could be Haymitch mentoring Katniss in a more personal way outside of the Hunger Games. Maybe he teaches her survival skills that are not just for the arena, like how to deal with the Capitol's political games in their district. Another could be a story where they form an unlikely alliance to change the rules of the Hunger Games from within. For example, they work together to convince the Capitol to make the games more humane.
Peeta could be a great addition. He already has a complex relationship with Katniss in the original story, and adding Haymitch to the mix could create some really interesting dynamics. For example, Haymitch could be the one to help Peeta and Katniss better understand each other's motives during the games.