It could also be that Snape's claim is part of a larger scheme. Maybe he is trying to use Hermione's intelligence and magical abilities to defeat a new dark force. Hermione, in the process, might learn a lot from Snape about the darker aspects of magic and how to use them for good, which would be a major character development for her.
One possible plot development could be that Snape's claim over Hermione creates a great deal of conflict within the wizarding world. The Order of the Phoenix might see it as a threat or a strange alliance. Hermione herself could initially resist but then start to understand Snape's motives, which could be related to protecting her from a greater danger.
One possible plot development could be that Sirius becomes a sort of protector for Hermione. He might use his knowledge of the wizarding world and his own skills to keep her safe from various threats. For example, if there are dark wizards after Hermione due to her intelligence or her connection to Harry, Sirius could step in and fend them off.
Another development might be the reaction of their friends. Harry and Ron might be initially skeptical or even opposed to this situation. There could be a lot of tension within the group as they try to come to terms with what it means for Hermione to be claimed by Remus. It could also lead to some rifts in their friendships at first.
The plot could involve the mistletoe having some sort of magical effect. Maybe it makes Snape and Hermione relive certain memories. As they do, they start to understand each other better. For instance, they might see how they both overcame difficulties in their pasts, and this new understanding could bring them closer together.
It could also be that Dolohov's desire for Hermione causes a rift among the Death Eaters. Some might see it as a distraction or a sign of weakness. This internal conflict within the Death Eaters could then be exploited by Hermione and her allies to their advantage in the fight against the dark side.
For Hermione, she might develop a more empathetic side towards Snape. She could start to understand his past traumas and the reasons behind his cold exterior. This could make her less judgmental and more open - minded. As for Snape, he could soften up. With Hermione's influence, he might show his more vulnerable side and let go of some of his grudges, especially towards the students he disliked at Hogwarts.
Perhaps Snape discovers Hermione's extraordinary intelligence in a new way, which makes him excited. Maybe she solves a really difficult magical problem that he thought was unsolvable, and this newfound respect and admiration leads to his excitement.
One possible plot could be that they have a deep conversation about their past differences and how they overcame them. They might share their hopes and fears for the future. Maybe they start with a quiet dinner in their new home, just enjoying each other's company and reminiscing about how they fell in love despite all odds.
Well, one plot development could be that Hermione is initially shocked but then realizes she has feelings for Fred too. They then have to deal with the reactions of their friends, like Ron being a bit miffed at first. Another could be that Hermione rejects Fred's proposal at first, but as the story progresses, she sees how much he truly loves her and changes her mind.
One possible reason could be a misunderstanding. Maybe Hermione thought Snape was involved in some dark plot against her friends. In the wizarding world, there are often secrets and deceptions, and if she got some false information, it could lead her to take such drastic action.
Perhaps the kiss is a moment of impulse for Draco, who has been secretly attracted to Hermione's intelligence and courage all along. Hermione, on the other hand, is initially shocked but then realizes she has some feelings for Draco too. Their relationship could then develop as they try to find common ground between their different houses' values. They might start working together on a project in the library, away from the prying eyes of their classmates, and slowly build a deeper connection through their shared love for learning and magic.