Well, as a centaur, Hermione would likely gain some centaur - specific magical powers. She could use her enhanced speed and strength to explore areas that were previously difficult for her as a human. And she might communicate with other centaurs in a way that reveals new magical secrets about Hogwarts or the Forbidden Forest.
One idea could be that Hermione turns into a centaur as a result of a misfired spell during a Defense Against the Dark Arts class. She could then struggle to adapt to her new form, having to deal with the physical differences like running on four legs and having a horse - like body. Meanwhile, her friends Harry and Ron would be trying to find a way to reverse the spell.
Well, in a Hermione Granger family reunion fanfiction, perhaps Hermione gets to introduce her wizard friends to her Muggle parents in a really fun way. Maybe they have a big dinner where they share magical stories that Hermione's parents are just amazed by.
She might discover new magical abilities that are unique to elves. For instance, elves are very good at household magic. Hermione could use these new skills to improve the living conditions in the Gryffindor common room. She could make the furniture more comfortable or keep the room cleaner without using much effort.
She might have more time to explore the library on her own. Without the distraction of other students at first, she could discover some really rare and powerful magic books. This could give her a head start in her studies and she might even come across some ancient spells that could be useful later in her adventures at Hogwarts.
Hermione could also get some extra study time in the library. With no other students around, she would have access to all the books she wants without any distractions. Maybe she would find some really rare and powerful spells or magical knowledge that would help her throughout her time at Hogwarts.
In this fanfiction, Hermione could find a way to communicate with the Greek goddesses. She uses her intelligence and magical skills to open a portal or perform a spell that allows her to have conversations with them. Through these interactions, she gains a deeper understanding of magic, life, and herself. Maybe she gets advice from the goddesses on how to deal with the challenges she faces at Hogwarts and in the wizarding world in general.
In some fanfictions, Hermione might betray Harry due to a misunderstanding. For example, if there were false rumors spread about Harry being involved in dark magic or having a secret, evil plan. Hermione, being a stickler for the rules and the greater good in the original series, might be misled into believing these rumors and thus betray Harry.
She could have her memories intact in her baby form. This would lead to some really funny moments. For example, she might be trying to get to the library but can't because she's just a baby. Her friends would be confused as to why she's so insistent on going to a certain part of the castle.
Another way could be through a potion gone wrong. In the wizarding world, potions can have all sorts of strange effects. If Draco was trying to brew a potion for some other purpose, like trying to gain an advantage in a competition or something, and made a mistake in the ingredients or the brewing process, it could result in him being transformed into Hermione. This would force him to experience life from her perspective, which could be a huge character - development opportunity for him.
In such a fanfiction, there could be a lot of chaos. Maybe Harry and Ron would be completely clueless on how to take care of baby Hermione. They might struggle with simple things like feeding her or changing her diapers. It could also be a really cute scenario where they try their best to protect her in this vulnerable state.