Sirius Black could also be part of it. He was Harry's godfather. He might have escaped from Azkaban earlier in this fanfic. He teams up with the Potters to rescue Harry. He could be the one who scouts out the Dursleys' house before the actual rescue operation, using his skills as an Animagus to stay hidden.
In this fanfic, the Potters could have faked their deaths all along. They come back to rescue Harry when they find out how horribly the Dursleys are treating him. They might bring some magical creatures with them to help. For example, a phoenix that can heal Harry if he has any injuries from the Dursleys. Then they take Harry with them on a magical journey to a hidden wizarding community where they can all be safe and happy.
In the fanfic, Snape might use his knowledge of the Dursleys' house layout. He may enter the house unnoticed, find Harry, and then use a Portkey to quickly get them both out of there. He could also have some sort of charm or potion that he uses to counter any magic the Dursleys might have used to keep Harry there, like a spell - breaking potion. And he may have planned the whole rescue very carefully, choosing a time when the Dursleys are least likely to notice, like in the middle of the night.
Hermione could be one to rescue Harry. She might have discovered some new spell or potion that allows her to bypass the protections around the Dursleys' house and get to Harry. Then she'd use her intelligence and quick thinking to get him out of there safely.
Maybe Draco finally understands that Harry is a victim of circumstances. The Dursleys' treatment of Harry is cruel, and Draco, having grown up in the wizarding world, realizes it's wrong. So he steps in to rescue Harry.
Maybe Percy uses his magic skills to create a distraction. He could conjure up some strange creatures outside the Dursleys' house. The Dursleys, being afraid of all things magical, would be distracted long enough for Percy to sneak in and get Harry out.
It could make Harry more empathetic. Snape is a complex character, and through his rescue, Harry gets to see a different side of him. This could make Harry more understanding of others' hidden motives and pain. He might start to look beyond the surface when dealing with people, which would be a great development for his character as he faces more complex relationships in the wizarding world.
A rogue wizard who has his own ideas about Harry's future could take him. This wizard might think that he can better prepare Harry for the fight against Voldemort than Dumbledore or the Order of the Phoenix.
Well, in some fanfic scenarios, Voldemort might have made a deal with someone who has access to the Dursleys' house. For example, he could have bribed or threatened a neighbor or someone who works in the area. Then, when the time is right, he enters the house under the guise of this person's help and rescues Harry. It could also be that Voldemort has some sort of inside knowledge about the protective spells around the Dursleys' place. He finds a loophole in those spells and slips in to save Harry.
After saving Harry, Snape may have to deal with a lot of mistrust from some people in Hogwarts who don't understand his motives. However, he might also start to form a closer bond with Harry, which could change the whole dynamic between them. This new relationship could lead to some unexpected alliances and enmities within the wizarding world. And if the Dursleys were to try and retaliate, Snape would have to constantly be on guard to protect Harry from any potential harm they could cause.