Another possibility is a new, unknown force from the Underworld. Maybe Hades has lost control over some dark entity that has grown in power and now aims to take over Olympus. This entity could be extremely powerful, with abilities that the demigods have never faced before. It would be a great antagonist as it would force the Percy Jackson characters to adapt and find new ways to fight in order to save Olympus.
A primordial being, like Chaos or Nyx, could also be the main antagonist. If they feel that the Olympians have become too powerful or are misusing their power, they might decide to wipe out the entire demigod race. Percy would then have to find a way to either convince them to spare the demigods or find a way to defeat them, which would be extremely difficult as they are among the most powerful entities in Greek mythology.
A new and powerful Titan who has been hiding and gathering strength all this time. He could be jealous of the Olympians' power and wants to take over. Percy would have to figure out his weaknesses and stop him before he causes too much destruction.
One interesting concept could be the crossover of the Percy Jackson world with the 'Olympus has fallen' scenario. Maybe the demigods have to deal with a political takeover of Olympus in a more modern, thriller - type situation, like in 'Olympus has fallen'.
It could be a new demigod who has a grudge against the Olympians. This demigod might be using Percy as a tool to carry out their assassination plans.
It could be a power - hungry Atlantean noble who wants to rule not just Atlantis but also the surface world. He sees Percy as a threat to his plans and tries to stop him at every turn.
A new and powerful demon that has emerged from the darkest corners of the underworld. This demon is bent on using Percy's connection to the overworld to break through the barriers between the two worlds and unleash chaos. It has powers that are different from what Percy has faced before, like the ability to manipulate the very essence of the underworld's environment.
A powerful Amazonian sorceress who has turned against her own kind and is now trying to use dark magic to take over the world. She could see Percy as an obstacle in her path and constantly try to defeat him.
Maybe it could be a demigod who has become obsessed with power through gaming. This demigod, let's say a child of Hades, discovers a way to use dark magic and combine it with gaming technology to try and rule over all the other demigods. He sees Percy as a major threat to his plans because Percy is so popular and has strong powers, so he constantly tries to undermine Percy at every turn.
The goddess Hera might also be a great antagonist. Since she has a history of interfering in the lives of demigods, she could be jealous or threatened by Percy's rebirth. She might try to stop him from reaching his full potential in his new life or cause trouble between him and his new allies.
A powerful demigod who has been corrupted by the idea of primordial power could be the main antagonist. They might believe that by allying with a primordial or obtaining their power, they can become greater than the gods. This demigod would then oppose Percy, who stands for the protection of the current order.