I started to write an application for the Joker, but then backed out based on the brevity of my soul Martian Manhunter post.

In short, it'd be an attempt to design a consistent version of the Joker without restricting his personality. For example, his former identity would be Alfred Striker (see Case of The Chemical Syndicate), a former soldier suffering from PTSD with chemical expertise who repurposed his military training for personal gain as the master criminal "The Red Hood." Somewhere in Year Two, Batman busts him before he falls into a vat of synthetic Dynesium.

He comes out, completely fed up with the predictable tragedy his life. So he wages a one man war against the mundane, intending and succeeding in  filling people with equal parts fear and disbelief. The nature of these schemes would be scattered across a broad spectrum, ranging from harmless and silly to abominable. Despite the fact that he is widely considered insane and irrational, he is a bona fide genius who consciously rejects orthodox patterns of reasoning.

Portrayal would most closely resemble Mark Hamill and Heath Ledger, followed closely by Cesar Romero. Despite efforts to disrupt everyday life and generally being considered a monster, he'd have a significant social media following and a podcast audio diary ("The Joker's Log").