Perhaps in the fanfiction, Aizawa gets One For All and decides to keep it a secret. He then starts training in isolation to master it. As he trains, he discovers new aspects of the power that are different from what previous users experienced, due to his own unique quirk and personality. He might use it to secretly protect his students from threats that are beyond the scope of his normal abilities.
One possible plot could be that due to some false accusations of improper teaching methods, Aizawa gets fired. His students then band together to prove his innocence. They collect evidence of his effective teaching, like how he has helped them improve their quirks and grow as heroes in training. Eventually, they manage to clear his name and he is reinstated.
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.
One possible plot could be Naruto suddenly obtaining the One for All power. He might struggle at first to control it as it's a very different kind of power from the chakra he's used to. His friends would be both amazed and a bit worried. Naruto could then try to incorporate this new power into his fighting style, perhaps creating new jutsu that combine his ninja skills with the raw strength of One for All.
He would likely become more confident in his abilities. Aizawa is already a capable hero, but One For All would give him an extra edge. This new power might make him a bit more assertive in hero situations, rather than just being the stealthy and observant hero he was before.
It could be a new administrator at the school who has a very different vision of how hero training should be conducted. This person might see Aizawa's methods as too old - fashioned or too lax, even though they are actually effective. So, they push for his dismissal.
In some fanfictions, Aizawa might be under the influence of a villain's quirk that makes him act against his will. So, he kidnaps Izuku, but later on, he realizes what he's done and tries to make amends. This could lead to a story full of drama and redemption.
He might lose his control over his own quirk for a while. Since his quirk is erasing others' quirks, if he's hit by a strange quirk, it could disrupt his own quirk's function.
Well, Bakugou might struggle to control One for All at first. It's a powerful quirk and he has his own explosive temper. He could accidentally cause a lot of destruction while trying to master it.
Well, it could be about Izuku confronting Aizawa over some misrepresentation in the fanfiction. Maybe Izuku doesn't like how Aizawa is being portrayed as too strict or unfair in the fic.
Perhaps the story involves the students of Class 1 - A learning valuable life lessons from Aizawa's husband. He might share stories about Aizawa's past that the students didn't know, which could strengthen their bond with their teacher. For example, he could tell them about how Aizawa overcame difficulties in his training days, and this could inspire the students in their own hero - in - training journey.