A third plotline could be that Hermione becomes an Animagus in secret to spy on the Death Eaters or other dark forces. She uses her new form to gather intelligence and outwit the bad guys. In this type of story, there would be a lot of sneaking around and narrow escapes as she tries to stay one step ahead of her enemies.
One common plotline is Hermione discovers her Animagus form on her own, without the help of others. It could be during a time of self - discovery or while she's in a dangerous situation and her hidden power as an Animagus emerges to save the day.
Another plotline might involve Hermione's Animagus form being something unexpected, like a rare magical creature. This could lead to all sorts of adventures as she tries to understand and control this new aspect of herself. For example, if she turns into a phoenix, she might have to figure out how to use its powers of regeneration and flight.