Given in the comics he's a complete mystery as to his origins prior to the chemicals and it's even been implied Joker might not even be human is it possible Joker could be like Red Jack from Doom Patrol and is some how a being that feeds on the pain and suffering of others? I mean I know some might not like the idea but I honestly think it would make Joker scarier if he was some cosmic or interdimentional being that causes chaos and suffering. I say this because it would really make the stakes much higher with Batman if he was just a man facing down against a far more powerful entity.
If they did go this route with Joker I think a good back story would be if he was a child of Trigon (I remember Raven trying to make Joker see his worst fears and his response was just laughter so it wouldn't be shocking if he was like her or rather a prototype Trigon discarded) and once was meant to act like Raven and like her resisted and while succeeding in beating Trigon was driven mad and became a demonic being that feeds on pain and suffering and wandered the world feeding on the pain and misery of others until coming across Bruce and his parents in the alley that night and seeing what Bruce would become decided to stick around out of amusement.
I like this idea because it really kind of reverses things especially when one considers what Bruce's crusade has cost him and how it's affected people like Jason Todd. I'd like to see a confrontation where Joker offers Bruce the chance to "ellevate" himself and brings up how Bruce has unintentionally caused suffering to those around him. Essentially something like this