Well, this might be pretty random - an idea inspired loosely by one of the K-Dramas my wife was watching.
Opening scene: A very ritualized murder occurs; the reader witnesses it, but it is not clear if they're an observer or seeing it through the eyes of the killer.
Next scene: Detectives are examining the scene when a man approaches them. He claims to be a psychiatrist who believes one of his patients either witnessed or committed the murder. Unless he is certain that the patient IS the killer, he can't share their name but can share details that came up in their sessions. He only talks to one of the police, a woman.
The doctor and the detective seem to have some chemistry between them but it is awkward at first.
Then a second murder happens, and all indications for the reader are that the psychiatrist IS the killer...
But when a third death happens, it also comes out that he could not have killed the first victim - and that there were other victims before that.
Half the victims turn out to be people who broke the law and managed to escape punishment. And all of them were patients of the psychiatrist...
His relationship with the detective grows - but they both start to become suspicious of each other...
Are they both serial killers? Or is some shadowy figure from their shared past really the culprit? Or is there something even stranger at play?