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.
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.
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.
There's also 'Growth Together'. This fanfic shows how Deku and Todoroki support each other during tough times at UA. They face challenges not only from villains but also from within the school. Their relationship develops as they help each other overcome these obstacles.
One idea for a Deku's Quirk fanfiction could be exploring what would happen if Deku's quirk manifested in a different way. For example, instead of having to gradually control One For All, he suddenly has full mastery from the start. This could lead to a very different story arc where he is immediately seen as a top - tier hero - in - training, causing envy and admiration in equal measure among his classmates.
One idea could be a fanfiction where Deku's quirk suddenly mutates. Instead of just having One For All, he starts to develop an additional power related to it, like the ability to share a fraction of One For All's power with his friends temporarily to boost their own quirks in a time of great need.
There are fanfictions where Deku teams up with unexpected characters. For example, he might partner with a minor villain who has a change of heart. This creates interesting dynamics and new story arcs that deviate from the original plot but still stay true to Deku's character.