Katsuki could become more empathetic. Since One for All is a power that has a lot of history and meaning, he might start to understand others better. For example, he may understand Deku's journey more deeply. He'll still be his bold self, but with a new layer of understanding and compassion added to his personality.
In some fanfictions, Katsuki gets One for All and it completely changes his relationship with Deku. Instead of rivalry, they start to train together more closely. There are also fanfictions where Katsuki uses One for All to save the day in a situation where no one else could. For example, when facing a powerful new villain that the other heroes can't handle. He might combine his natural combat skills with the power of One for All in a unique way.
If Katsuki got One for All in BNHA fanfiction, he would become an even more powerful hero. His already explosive quirk combined with the power of One for All could make him nearly unstoppable. He might have to learn to control the new power though, as it could be overwhelming at first.
One could be Izuku. He might be there to witness Katsuki's downfall due to bad karma. Izuku could be the one who tries to help Katsuki see the error of his ways, even though Katsuki has been unkind to him in the past. It would add an interesting dynamic to the story.
Maybe in the fanfiction, Katsuki has always been overconfident and underestimated his opponents. The bad karma could be that he faces a powerful enemy who completely outmatches him. He then has to struggle not only with the physical threat but also with the psychological blow of his own hubris. This would force him to re - evaluate himself and his actions.
Well, he could be at a skating event's after - party. He accidentally drinks too much champagne. As he gets drunk, he might mistake a famous skater for his coach and start asking for advice on his next routine. This would lead to some comical misunderstandings.
The plot could involve Yuri being hypnotized to overcome his stage fright. Maybe a well - meaning friend or a new coach discovers that Yuri has deep - seated fears that are affecting his performance. They use hypnosis to take him into a state where he can face those fears head - on. In this trance - like state, he relives his worst skating moments but with new confidence, and when he comes out of it, he's a changed skater, ready to take on any competition without hesitation.
One possible reason could be if Katsuki is rude to Izuku. Since Inko is Izuku's mother, she would naturally get mad at someone who is mean to her son. For example, if in the fanfiction Katsuki makes fun of Izuku's dreams or abilities in a particularly cruel way in front of Inko, she would likely become angry.
His character would likely become more responsible. Since One for All comes with a lot of responsibility, Katsuki would have to step up. He'd start to think more about the greater good rather than just his own goals.
One possible plot could be that Uraraka struggles to control the new power of One for All at first. She might accidentally use it in inappropriate situations, like floating everything in her dorm room. But as she trains hard, she gradually masters it and uses it to save her friends in a big battle against a powerful villain.