In the fan fiction, Snape may see Harry as a potential asset in the fight against the Dark forces. He knows that if Harry is constantly in danger from Vernon, it could weaken Harry both physically and mentally. So, to ensure that Harry can grow up strong and be able to face the challenges ahead, Snape decides to save him from Vernon.
It could be that Snape wants to spite Vernon. Vernon represents everything that Snape despises about Muggles who are cruel and unaccepting. By saving Harry from Vernon, Snape is showing his superiority over Vernon and also his power as a wizard. And of course, there's still that underlying reason of his love for Lily which makes him want to protect her son.
In this fan fiction scenario, Snape might use his knowledge of the Muggle world and Vernon's weaknesses. Snape could have found out some information about Vernon's business affairs or personal secrets. Then he blackmails Vernon into leaving Harry alone. By doing this, he effectively saves Harry from Vernon without having to use too much magic and draw unwanted attention.
In this type of fanfiction, Snape could simply intimidate Vernon. Snape has an air of mystery and a certain power about him. He might show up at Vernon's doorstep, give Vernon a cold stare, and with his reputation as a powerful wizard, Vernon might be too scared to oppose him. Snape could then just take Harry without much resistance from Vernon.
If Snape witnesses Vernon abusing Harry in fan fiction, he might use it as an opportunity to gain some leverage over Harry. Snape could offer to keep quiet about the abuse in exchange for Harry doing certain things for him, like getting good grades in Potions. However, this is a rather cynical view and goes against Snape's more complex character who deep down has some good in him.
Snape might do it out of his love for Lily. Since Harry is Lily's son, he feels a sense of obligation to protect him.
One motivation could be simple friendship. Despite being from different schools, they might have developed a bond during the Tri - Wizard Tournament. Viktor could see Harry as a worthy opponent and not want to see him die in the second task.
One motivation could be self - preservation. Draco might realize that if Voldemort kills Harry, it will lead to an all - out war that could destroy everything he knows. By saving Harry, he hopes to find a more peaceful solution and protect his own family and the wizarding world in a broader sense.
In this fan fiction, Snape might adopt Harry because he realizes that Harry has a lot of potential that is being stifled at the Dursleys. He could take Harry to a secret location and train him not only in magic but also in self - defense and survival skills. Snape would have to deal with his own complex feelings towards Harry, as he has both resentment and a sense of obligation. And Harry would have to adjust to living with Snape, who is not exactly the warmest person. It could be a story of growth and understanding between the two.
Snape's view of Harry would likely soften. He would see that Harry has a difficult home life, which could make him more sympathetic towards Harry. He might stop being so harsh in his treatment of Harry at Hogwarts.
Eric might also see Tris as an asset to his own plans or goals. If he wants to gain more power or influence within their community, he might think that by saving Tris from Peter, he can earn her loyalty and have her on his side. And Tris is known for her strong will and skills, which can be useful to Eric.
Well, Naruto has a strong sense of justice. He can't stand to see anyone being bullied, especially someone he cares about like Sakura. He might also want to prove himself. By standing up to the bullies, he shows that he's not the weakling some people think he is.