A typical scenario in such a fanfic is when Snape steps in to shield Harry from the malicious rumors and false accusations spread by other students or some of the Hogwarts staff. Snape, using his position and influence, makes sure that Harry is not wrongly punished or ostracized. There could also be a scenario where Snape helps Harry understand his parents better by sharing some memories or stories that he has of them, which helps to build a unique bond between them.
One common scenario is Snape protecting Harry from the Dark Arts attacks within Hogwarts. Another could be Snape helping Harry with his studies privately, especially in potions where Snape is an expert.
One common scenario is Snape protecting Draco from the other Death Eaters. Since Draco is young and somewhat naive in the ways of the Dark Arts and the Death Eater world, Snape steps in to keep him safe. Another scenario could be Snape helping Draco with his schoolwork, especially in Potions. Snape, being a master of Potions, would be able to guide Draco and boost his confidence in that subject.
There could be a situation where Harry is being bullied by some students from other houses. Snape, despite his usual cold exterior, steps in and scolds the bullies. For Draco, if he gets into trouble with other Slytherins over some internal house politics, Snape would quietly resolve the issue. In addition, Snape might offer to tutor them personally. He would give Harry extra help with his Patronus charm, knowing its importance, and for Draco, he could teach him some advanced potions techniques that are not taught in regular classes.
One common theme is redemption. Snape is often seen as a character in need of redemption in the original series, and taking care of Harry can be a way for him to achieve that. Another theme is the exploration of family. It shows a different kind of family dynamic than the traditional ones in the Harry Potter world. And there's also the theme of sacrifice. Snape might have to sacrifice his own interests or safety to protect Harry.
Well, it could be about Snape feeling a sense of duty. Maybe after Harry loses his sight in a battle against the Dark Arts, Snape, despite their past differences, steps in. He might start by teaching Harry new ways to navigate Hogwarts using magic that doesn't rely on sight, like advanced sonar - like spells.
Well, at first Harry might be very suspicious. But as Snape shows consistent care, Harry could start to see him in a new light. Maybe he realizes that Snape has more layers than he thought. He might begin to understand that Snape's past actions were more complex than just being mean to him.
Often, in the fanfic, it could be that Harry is injured during a Quidditch match. Snape, despite his dislike for Harry in some ways, realizes the importance of Harry to the wizarding world and heals him. There could also be a situation where Harry is affected by some dark magic in the Forbidden Forest. Snape, who has a deep understanding of dark magic, is the only one who can counter it and heal Harry. It might also happen that Harry is suffering from the after - effects of using powerful magic, and Snape uses his own unique magic to heal Harry's drained energy.
One possible scenario is that Anko takes Naruto on special training missions in dangerous and unexplored areas. This would not only strengthen Naruto's skills but also build their bond. Another could be Anko helping Naruto deal with the pressure of being the Jinchuriki, perhaps by sharing her own experiences of dealing with difficult things in the ninja world.
A common plot element is Snape's initial reluctance. He might be forced by Dumbledore or some other situation to take care of Harry. But as he does, he starts to see Harry in a different light. For example, in many stories, he realizes that Harry is just a vulnerable boy, not just James Potter's son.
Maybe Harry tries to feed the baby cousin some magical baby food. He could make funny faces to get the baby to open their mouth and eat. It would be really adorable to see the baby's reaction to the new flavors.
One common scenario is when Naruto gets injured during a mission. Sasuke, being the one to take care of him, uses his skills to heal Naruto or at least keep him stable until proper medical help arrives. Another scenario could be Sasuke protecting Sakura from an enemy's attack, perhaps even sacrificing himself a bit in the process. And sometimes, Sasuke might help Sakura in her medical research, providing her with rare herbs or knowledge he's acquired during his travels.