Heavy Rain's director David Cage talked about the game way back during LGC, and something quite interesting fell through the cracks: The main character of the game can die, however the players won't be face with a GAME OVER screen:
"I can't really tell you too much about what the story's about or how it's going to work with the characters, all I can tell you that your character -- the main character -- can die, and the story will continue...You can continue to play, without this character, of course." - David Cage, Heavy Rain Director
What's more, this wouldn't be a side story, rather a continuation of the main story. Talk about having options!