The number of endings can be infinite. Quantic Dream have stated you make the story and they mean this. There are literally hundreds of ways each scene can end, this can be altered by what events you trigger, how well you do in quick time events e.g. If you avoid getting hit twice but then get hit on the 3rd it may take the fight somewhere entirely different. If you die that changes the overall ending. This game is so complex, story lines arc and bend the very second you enter that scene. With over 60 scenes in the game and so many ways to manipulate and change what you do and what you see in each scene, there is almost absolutely no pre-determined ending to this game. My answer is infinite.

Oh and the way i'm going to play is when i start i will decide who i want to make it to the end. This character will be my main character/actor, from here the rest will be relegated to supporting roles. These are characters that can die and may die just because i choose them to die. If it all works out and my main character doesn't die, they like a real movie should uncover who the Origami killer is. I am going to play this game like i am the director and as if i have written the script. The second the scene starts i will know if this is a place i want my support character to survive or if i want them to die.

I've got to say, from what I've seen from the game so far, I don't hold out for more than about 3-5 proper endings (One or all of the characters dying with the story incomplete is not an ending in my book). There are certain events that seem to be pre-determined no matter how you reach them in a given scene, and no game can be pre-programmed with an infinite number of cutscenes for the story to develop in an entirely different way from each little minor action.

The more choices there are within the story of a game, the lower the emotional resonance of each choice. And if Farenheit is anything to go by, much of the "freedom" you are given is an illusion. For instance you could try playing poorly as the detectives, to give the killer more leeway in the next scene, but all that would happen would be your mental state reducing until you quit the police force/went mad, at which point the game would end. There were only a handful of true story changing choices in the game, and only three proper endings. I'd guess this would be the same thing on a slightly grander scale.