Well, one plot point is that Hermione often has to keep her mission a secret. If other people, especially those who don't trust Snape, find out what she's doing, it could cause a lot of problems. Also, there's usually a part where she has to face the consequences of changing the timeline. For instance, some relationships might be altered, or new threats might emerge. In some fanfictions, she also has to deal with Snape's initial disbelief or hostility when she tries to save him. He might not trust her motives right away, and she has to prove that she's really there to help.
A lot of these fanfictions explore how Hermione's personality is shaped by her parents. For instance, she could have Snape's sarcastic wit and Narcissa's poise. There are often plot points about her being ostracized by some Gryffindors who don't trust her new heritage. And she may have to prove herself more in the wizarding world. The mystery around her parentage might also be a big part of the plot, with her slowly uncovering the truth about how she came to be the daughter of Snape and Narcissa.
One common plot point is the secrecy itself. They often have to hide their relationship from others in the wizarding world. Another is the conflict that arises from their different personalities and backgrounds. For instance, Snape's dark past and Hermione's more positive outlook.
In fanfiction, the Time - Turner can be a tool to bring Hermione and Snape closer. For example, if Hermione uses it to help Snape with a past event, he may start to trust her more. This newfound trust can change their relationship from one of animosity in the original story to a more collaborative and understanding one. They might share secrets and knowledge that they wouldn't have otherwise.
Another plot point could be Hermione standing up for her friends. Like when Snape is being overly harsh on Harry or Ron. She steps in, not afraid of the consequences. This highlights her loyalty and her sense of justice. In some fanfictions, this might lead to a power struggle between Hermione and Snape, where she has to use her wits to avoid getting into too much trouble with the strict professor.
The theme of sacrifice also appears. Snape may have to sacrifice his own safety, reputation or his standing within the wizarding world to save Hermione. This shows his selfless side that might have been hidden before. And in some fanfictions, this sacrifice is what ultimately changes the course of the story and the characters' development.
One common plot point is the revelation of the truth. There's often a moment where either Snape or Harry discovers the truth about their relationship. Another is Snape's internal struggle. He has to deal with his long - held feelings for Lily and his new - found fatherly feelings for Harry. Also, there may be a change in how Harry views Snape. Instead of seeing him as a strict and often unfriendly teacher, he starts to see Snape in a new light, as his father.
One common plot point is that Harry often has to find a way to get past the Dementors in Azkaban. He might use the Patronus charm in a new and creative way. Another is that he usually has to overcome some sort of magical obstacle or security measure in the prison. And of course, there's always the emotional reunion between Harry and Sirius.
One plot could be Hermione using the Time - Turner to go back and change Snape's perception of her. Maybe she tries to show him that Gryffindors can be worthy allies. Another could be that Snape discovers Hermione's use of the Time - Turner in a way that wasn't in the original books and they end up working together secretly to stop a new dark threat.
Another plotline might involve Snape discovering Hermione's use of the Time - Turner and initially being suspicious of her motives. But as they interact more in the altered timeline, they end up forming an unlikely alliance. They could work together to uncover a long - buried secret about Hogwarts that was lost in time.
A common plot element is the discovery of Hermione's situation. Usually, Remus somehow becomes aware that Hermione is in danger or being abused. It could be through his own observations, or maybe Hermione reaches out to him for help.