It could be that an anonymous assassin is the suspect. This assassin could have been hired by someone who wants Percy out of the way but doesn't want to get their hands dirty. Or perhaps a possessed character could be the suspect. They have no control over their actions when they kill Percy as they are being controlled by a malevolent spirit.
The butler could be a suspect. In many murder mysteries, the butler is often initially suspected. Or perhaps a jealous rival. If there's some sort of competition in the story, a rival might have a motive to commit murder.
A rival law enforcement agency member could be a suspect. Maybe they see Deeks as a threat to their own investigations or operations and decide to take him out. It could be a power play within the world of law enforcement.
It could be an old enemy from Beckett's past. Maybe someone they put in jail a long time ago, who has now been released and is seeking revenge.
It could be a random act of violence by a criminal who was in the wrong place at the wrong time. There are some bad elements in the area where Blaine was and they just targeted him without any specific reason other than opportunity.
One potential character could be a wise old hermit who lives in a secluded part of the paradise. He could offer Percy valuable advice and knowledge about the secrets of the paradise.
In a British crime story, it could be the butler. They are often a suspect in these types of stories. Maybe a jealous business partner of the victim could also be a suspect. And don't forget the mysterious neighbor who always seems to be lurking around.
He could find some minor gods or goddesses who have been banished to Tartarus. They might see Percy as a way to get revenge on the Olympians or simply a means to escape. Another potential ally could be some of the more intelligent monsters, like a centaur who has been there for a long time and has knowledge of the place.
A new healer character could be added. This character could be both intrigued and a bit wary of Percy's blood - bending ability and could try to help him understand it better.
A centaur who has knowledge of ancient prophecies involving both Percy and Artemis could be added. The centaur could act as a guide or a mentor to them during their adventure. He could provide crucial information about the enemies they are facing and how to use their combined powers effectively. For example, he might know of a weakness in a powerful foe that only Percy's unique abilities and Artemis' lunar powers can exploit.
It could be an ex - lover. Maybe they had a bitter break - up and the ex - lover was filled with jealousy or revenge. Another suspect could be a business rival if Amy was involved in some sort of cut - throat business environment.