One possible plot could be that Rabastian has some dark motives related to Hermione's magic abilities. Maybe he wants to use her knowledge of spells and potions for his own evil schemes. He could hold her in a secret location, and Hermione would have to use her wits to try and escape or send out some sort of magical signal for help.
Well, perhaps Rabastian kidnaps Hermione as a way to bargain with the Order of the Phoenix or Hogwarts. He might think that her value to those groups is so high that they would be willing to give him something precious in return, like a powerful magical artifact or certain information. Hermione, in the meantime, would be trying to figure out his weaknesses while being held captive.
Dumbledore could play a crucial role in her rescue. He has great wisdom and powerful magic. He might sense that Hermione is in danger through his magical connections. Then he could send some of the more skilled members of the Order of the Phoenix, like Sirius or Lupin, to find and rescue her. They would be able to use their combat skills and magic to overpower Rabastian.
One possible plot could be that the other characters, like Harry and Ron, immediately start a rescue mission. They might search for clues about where Dolohov has taken Hermione. Maybe they discover that Dolohov is working for a more powerful dark wizard who wants Hermione for her knowledge of magic. Then they have to face various traps and dark spells to reach her.
One possible plot twist could be that Hermione uses her intelligence to outwit Dolohov even while kidnapped. Maybe she manages to leave hidden clues for her friends to find her. Another could be that Dolohov has an ulterior motive other than harming her, like using her as a bargaining chip in the wizarding war. Or perhaps Hermione discovers a hidden power within herself during the time of her captivity that helps her escape.
One possible motive could be to use Hermione as a bargaining chip. Maybe Narcissa wants to exchange her for something important to the Death Eaters, like information or the release of a captured Death Eater. In the wizarding world of 'Harry Potter', such power - play is not uncommon among the dark forces.
One possible motive could be to gain an advantage over Harry Potter. Hermione is Harry's closest friend and a very intelligent witch. By kidnapping her, Draco might think he can use her as a bargaining chip to make Harry do something or to get information from her that could be useful to the Death Eaters. Another reason could be jealousy. Draco has always been in competition with the Gryffindors, and Hermione's intelligence and skills might make him envious to the point of doing something drastic like kidnapping.
A common plot twist is that Hermione actually has a hidden power or ability that she reveals during her captivity. For example, she might be able to use a type of magic that Draco and his associates didn't expect, which gives her an upper hand in the situation. This could lead to a change in their relationship dynamic, from captor - captive to something more like equals.
Obviously, Harry Potter could be the one to save her. He has a strong bond with Hermione and is very brave. He'd stop at nothing to rescue his friend. He might use some of his unique magical abilities, like his connection to Voldemort, to find her.
Perhaps a plot twist could be that Draco is under the influence of a dark spell when he kidnaps Hermione, and as she tries to break the spell, she uncovers a conspiracy within the wizarding world. Or it could be that the kidnapping is a ruse set up by Hermione herself to infiltrate the Slytherin group, but Draco doesn't know it and things spiral out of control.
One possibility is that Artemis has been misinformed. Some enemy of Percy has tricked her into thinking that Percy is a danger to the demigods. So she kidnaps him to stop him from causing harm. But as she keeps Percy captive, she slowly realizes that she has been deceived when Percy starts to explain his side of the story and the real threats he has been fighting against.
The plot could involve the Phantom seeing Christine as his only salvation from his lonely and tortured existence. So, he kidnaps her with the intention of making her understand his world. He may show her his musical creations, hoping she'll come to love him in return. However, Christine might be initially terrified and try to escape.