Another possibility is a character who has a personal vendetta against Peter. Maybe someone who was affected by Peter's actions in the past, whether they were good or bad. This character could be out for revenge and constantly try to thwart Peter's plans, adding a lot of drama and tension to the story.
Perhaps some powerful organizations or institutions. If Peter is trying to disrupt the status quo, these entities that benefit from the current system would be his antagonists. They might see him as a troublemaker and try to stop him. They could use their resources and influence to try and take Peter down, creating a lot of conflict in the fanfiction.
Often, other symbiotes can be the main antagonists. For instance, Venom himself might see Anti - Venom (Peter) as a threat and constantly try to attack him. Venom could be jealous of the power that Anti - Venom has or simply view Peter as an enemy because of the different nature of their symbiotic relationships.
Well, in this kind of fanfiction, Peter might have a morally ambiguous nature. He could be someone who doesn't always follow the traditional rules of heroism. For example, he might use unorthodox methods to achieve his goals. Maybe he's more self - centered than a typical hero and focuses on his own interests while still having some redeeming qualities that make readers root for him.
One possible antagonist could be Sabretooth. He might see Wolverine's newfound fatherly relationship with Peter as a weakness and try to use Peter to get to Wolverine. Sabretooth could be jealous of the bond Wolverine is forming and want to destroy it.
Doctor Octopus could also work well. He might have a vendetta against the school because of some past incident. He could use his mechanical arms to attack the school, and Peter Parker would have to lead the defense. His intelligence and his ability to control those arms make him a formidable foe.
The White Witch could be resurrected as the main antagonist. She was a powerful and evil force in the original Narnia stories, and her return would pose a great threat to Peter and Narnia once again.
A new and original antagonist could be a rogue psychologist who has developed a powerful hypnosis technique. This character might be jealous of Peter's abilities and want to use hypnosis to take over his mind and use his powers for their own gain. Or it could be a secret organization that wants to use Peter as a weapon, and they use hypnosis as a means of control.
Stain could be considered as an anti - hero in fanfiction. His extreme views on heroes, while not entirely acceptable, could be delved into deeper. He believes that only true heroes should be recognized and is willing to take extreme measures to prove his point. A fanfiction could explore a different side of him, perhaps one where his actions are more nuanced.
The Green Goblin could be a main antagonist. He's known for causing chaos in New York City, and a building collapse would be right up his alley. He could be targeting the building for some strategic reason, like trying to get to Peter Parker or to create general mayhem.
Maybe it's a group of intergalactic criminals who are after the power that Peter Parker has as a 'child of the universe'. They could be stealing artifacts from different planets to gain more power and they see Peter as the ultimate source of power that they need to complete their collection.
The Green Goblin could be a main antagonist. He might see Peter's control of Alchemax as a threat to his own criminal empire and try to take over the company or destroy it. Another could be Doctor Octopus. With his brilliant mind, he may want to use Alchemax's resources for his own mad experiments.