One interesting aspect could be the different interpretations of the characters' powers. In fanfiction, the author might explore new ways Deku uses his One for All ability against Overhaul's powers. It can also show different battle strategies that might not be in the original manga or anime.
You can try looking on fanfiction websites like Archive of Our Own (AO3) or FanFiction.net. These platforms usually have a wide variety of fanfictions, including ones related to 'Deku vs Overhaul'. Just use their search functions to find what you're looking for.
One idea could be exploring Overhaul's backstory in more depth. Maybe show his childhood and what led him to become the villain he is. Another could be a redemption arc for him, where he teams up with the heroes against a greater evil.
One idea could be to explore Overhaul's backstory in more detail. Maybe show how he became so obsessed with 'perfection' and order. For example, you could create a scenario where he had a difficult childhood in a chaotic environment, which led him to strive for the extreme control he desires in the series.
In a Deku villain fanfic, perhaps Deku could form an alliance with some of the existing villains in the Boku no Hero Academia world. He might see potential in them that the heroes overlook. He could team up with Shigaraki, believing that together they could reshape the world into a more 'fair' place, according to his now - twisted view.
Secondly, introduce other characters that can act as catalysts for Overhaul's character development. It could be a hero who challenges his beliefs, or another villain who has a different view on things. Their interactions can bring out different sides of Overhaul. For instance, if he meets a hero who has a very loose and carefree attitude towards life, it could really grate on Overhaul's sense of order and make him question his own rigidity.
In fanfiction, a quirkless Deku often has to rely more on his wits. Canon Deku got One For All, but in fanfic, he has to find other ways to be strong. For example, he might study different fighting styles more intensively.
Toga could be an ally. Since she has her own complex relationship with the idea of heroes and villains, she might find Deku's transformation interesting. She could provide some of her unique skills, like shape - shifting, to help Deku in his villainous plans. Additionally, Twice might also join them because of his loyalty to Toga and his own sense of being an outcast in the hero world.