Some of the more corrupt and power - hungry members within the mafia that Percy joins could be antagonists. They might not like Percy's attempts to change things or might be jealous of the skills he brings. For example, an old - school mafia capo who doesn't trust this new kid with all his strange abilities.
Perhaps there are some supernatural forces working against Percy in the mafia world. Maybe there are cursed artifacts or dark magic users that the mafia has unknowingly angered, and Percy gets caught in the middle. Since he's used to dealing with Greek mythology - related threats, this new type of threat in the mafia context would be a whole different ballgame for him.
Maybe some of the more malevolent Primordials themselves could turn out to be antagonists. If Percy refuses to do their bidding or stands in the way of their plans, they would oppose him. Also, there could be ancient creatures that are awakened by Percy's presence among the Primordials and they see him as an intruder to be eliminated.
Maybe Percy uses his demigod powers in the mafia world. He could be really good at combat and strategy from his experiences fighting monsters, which would give him an edge in the mafia's dangerous activities.
The Titans could still be antagonists. In the Percy Jackson universe, they are powerful and malevolent. A princess in a fanfic might have to face their wrath as they try to overthrow the gods and take over the world. They would see the princess as a threat, especially if she is allied with the gods or has some special power that could stop them.
The Titans could be great antagonists. They might see Percy as a threat because of his connection to Thanatos and the power it could potentially give him. Also, some rogue underworld creatures, like powerful demons or vengeful spirits, could oppose Percy. They may not want Thanatos to have a more powerful influence through Percy.
Some of the more powerful and vengeful spirits in the Underworld itself could be antagonists. They might not want an outsider like Percy to be the Champion of Hades. They could try to undermine him at every turn, like spreading false rumors about him among the other Underworld denizens or directly attacking him when he's vulnerable during his quests in the Underworld.
Some of the primordial gods who are jealous of Chaos's newfound relationship with Percy could be antagonists. They might view Percy as an upstart and try to undermine his position. For example, Erebus could try to create chaos in Percy's life in a more malicious way, not in the way that Chaos intends.
The Titans could still be a major threat. Even though they were mostly defeated in the original series, some of their followers might see Percy's new role in Atlantis as a threat to their plans for chaos. They could try to undermine Percy's position in Atlantis and use the underwater city as a base for a new uprising.
It's possible that the main antagonist is a new mythological creature that has the ability to manipulate minds. It has lured Percy and other demigods to the mental hospital and is slowly driving them insane in order to feed off their fear and chaos energy.
The Titans could still be antagonists. They might see Percy as a threat in his new role as the champion of Hecate. Another could be some rogue demigods who are jealous of Percy's new power and want it for themselves. And there could be magical creatures that have been corrupted by dark magic and oppose Percy's efforts to bring balance with Hecate's magic.
There could also be some ancient monsters or spirits that are tied to Olympus' existence. They might rise up to defend it because their own survival is linked to the continued existence of Olympus. These could be powerful beings that Percy has never faced before, adding an extra layer of danger to his quest to destroy Olympus.