Venom could be a formidable antagonist. He might be attracted to the chaos and different powers at Monster High. He could start infecting some of the students, turning them into his minions. Additionally, a group of anti - monster humans from Peter's world could find out about Monster High and decide to invade it. They see the monsters as a threat and want to 'cleanse' the school, which would put Peter in a difficult position as he has to protect his new friends from his own kind.
Well, perhaps there's a science experiment gone wrong at Monster High that creates a rift in the multiverse, pulling Peter Parker into their world. He teams up with Frankie Stein, who is also interested in science. Together, they try to find a way to close the rift while also dealing with the social drama at Monster High. The vampires might be causing trouble because they don't trust an outsider like Peter, but in the end, he wins them over with his heroic deeds.
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.
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.
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.
The main antagonists could be the official Avengers themselves. Since Peter Parker has joined the rogue Avengers, the main Avengers group might see them as a threat to the order they are trying to maintain. They could try to stop the rogue Avengers from achieving their goals, which would put them in direct conflict with Peter and his new allies.
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.
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 Green Goblin is often a common antagonist. His chaotic nature and vendetta against Spider - Man would still be a major threat even if Peter is reborn. He might come up with new and more devious plans to take down Spider - Man.
In some fanfictions, Zemo - the one who originally stirred up trouble in the movie Civil War - could still be a major antagonist. He might target Peter specifically to get to Tony or use Peter's inexperience against the heroes.