I don't think you should give the player that sort of choice before they have any context. If you wanted, though, it could be a password-based thing, where you enter a code that you can get from the end of the game or from a walkthrough or something, so that if you already know about it and want to get it without beating the game, you can.

Either that, or don't give them the choice and make it unlock after you beat the game. I just don't think it should be a choice at the start of the game type thing.

Flat out asking is a very bad idea. It's very forced, breaks the immersion. I mean, would Meryl's death in the bad ending of the original Metal Gear Solid have nearly the emotional impact if it happened because there was a pop-up prompt asking which ending you wanted?

Perhaps allow for a new game+? After getting the "default" ending, you can get an inventory item that defeats some otherwise unbeatable boss or acts as some sort of quest item. Or perhaps allow extra dialogue or interaction options that assume the player or character already knows something the story hasn't revealed yet, as Pokemaniac suggested.

Since I haven't played Act III yet because I've lost my save data from the first two acts and I want to wait for the Complete Edition, I'll use a more abstract example. Alice sees Bob and has two dialogue options: say hello or wave goodbye. After Alice chooses one of the options, Bob kills her with the knife he had hidden behind his back. On playthrough two, Alice sees Bob again but now has a third option: she can become suspicious and ask Bob what he has behind his back. Bob may or may not kill her after that, but the story thereafter changes. Bob's attack remains a surprise on the first playthrough with no hint that it could be somehow avoided, but on the second playthrough the option is there without requiring a dead squirrel in the player's inventory or some cumbersome password.

Then there's Cave Story's method: it will tempt you to go after the "default" ending by offering upgrades that the player can turn down. The vast majority of players, unless they're using a guide, are going to accept the upgrade. Although Cave Story doesn't make it clear even after finishing the game that those choices had any impact on the story, once the player knows they matter he can go back and get that secret ending, even if he had already deleted his old save data. It doesn't have to be upgrades per se, but it should be something that really, really encourages the "correct" choice the first time around: a reward of some sort with an option to go back and accept it even if you turn it down the first time. Accepting some party member into your party, not knowing that he will betray you. Traveling to some town to complete some objective, not knowing that you'll be trapped there while something dire happens in your absence. Or completing some easy quest not knowing that it actually helps your enemy.

Again, I don't know (or want to know) what happens in Act III, but there has to be SOME alternative to OOCly asking the player what ending he wants. Even if you highly suggest the player select a certain option, you're giving him a big red button and telling him not to push it.

Lemme see if I'm understanding you properly: for people that don't have a save file anymore (lost it or whatever) but did finish Act III, you want to give them access to New Game+ materials straight from the get go.

For that, I'd use that "Cave Story" suggestion as opposed to directly asking the player if he wants the "plus" version of the game (I know I'd be tempted to pick that option even if I hadn't beaten the game already). Since I haven't played Act III I can't provide an example, but altering the very beginning of Act I to allow for some action that only someone that had finished Act III would think to do, that could act as a "cheat code" to unlock the New Game+ content. As an abstract example, maybe if Alice knew that killing the first enemy encountered in the game caused something bad to happen at the end, intentionally losing that hard-to-lose fight would unlock the New Game+ content as opposed to bringing up the Game Over screen. If no one can think of anything clever like that, you could ask something like who was really the big bad guy all along and provide a grid of characters to choose from. After making a choice, the player receives no confirmation of whether he was right or wrong, only knowing whether or not he unlocked the extra content when he finally gets to Act II and starts seeing the extra choices.

And then there's always the Konami Code.

If I'm misunderstanding you again, please correct me.

wakka wakka again. (sorry for using you as a guinea pig for testing Latest Posts again).

multiple endings, awesome! XD and I suggest making it to where you have to play through the main story first, then you can choose between one of the other to, and go straight to where that side version starts the changes.