Well my idea is the following. Most games have difficulity levels: Easy, Normal, Hard. But how about a game (ex: FPS) that had something like:

• Clear 'em out
• Just a little closer
• Keep 'em coming
  And "level" was just a different approach to playing the game. In the first one, the goal of the player was to clear out each room. In the second one, the player lays traps, sneak attacks, and snipes the enemies. In third one, continuously respawn varying ways (waves, every 5 minutes, random places, etc). This lends itself to more of a pick and play style of playing but at least there's instant variety in the gameplay.
  
  Has this been done before?

That sounds interesting, but one big problem for me is seems it requires the player to learn a lot of new knowledge (the operation, game play, goals, etc).

The player wants to play, not to learn.

The most successful game, like Super Mario Bros, is very very simple to play, very little to learn, the goal is always the same -- reach the flag pole in each level.

However, if you can give proper guide for any new knowledge so the player will not aware he is learning, that's another story. But that will be looking like a multiple tasks system, which is not new.

In one way or another this objective altering difficulty level has been introduced by a number of games. Off the top of my head - Outlaws. An oldie (and I'm sure there are better examples), but what happened there was that on low difficulty settings you could essentially rush in guns blazing and wipe everyone out. On higher levels of difficulty, where you could be killed in a shot or two, you had to adopt hit and run tactics, plus also play a bit of hide and seek. Looking even further back, your idea on Keep'em coming can be compared to Doom 2 Nightmare difficulty level, where fallen enemies would resurrect after a minute or two, making you face a constant horde of foes.

So this has been explored to a certain degree, but it is certainly worth taking further. Altering gameplay mechanics (or preferred ones anyway) on different difficulty settings might prove to be great at promoting game's replayability.

I like the concept, interesting thought! I can't personally think of any examples where a choice has been explicitly offered, although as mentioned some games do cater for this. One example might be System Shock II, where players chose between 3 different character types who had to approach the game very differently to be successful, but then allowed the player to further customise and approach problems however they saw fit.
One potential downside to this would be an increased workload on the level designers, as providing a good experience to players in each mode would require either a) producing different levels for each mode, or b) having all modes played in the same levels, and ensuring said levels provided a good play-experience for players using each style. A level suitable for running in guns blazing is not necessarily fun or suitable for a player who prefers to take a stealthy approach, and a level suitable for the stealthy player might be too "busy" and cluttered for a run-and-gun player to be effective.


Some players may also not have a clear idea of how they would like to approach the game before they begin play, or might think they're well suited to stealthy game-play but in reality be pretty openly trying to gun down their enemies; if the levels and difficulty are finely tuned for a certain style of play these plays may suffer as a result and end up finding the game to be impossible or feel it is unfair.

The purpose of difficulty levels is to let both weaker and stronger players win the game while giving their best. It has nothing to do with playing style. So you can't really use it "instead".

I'm thinking about the Thief games where difficulty would add extra objectives. I've no idea if it also made the enemies harder. It would be things like "get xyz amount of gold", "Don't kill anyone" that kind of thing. A little less than your idea but on a similar theme.

The Zuma games by Popcap are sort of an example of this. In the main game mode you play to a certain point goal. Once you achieve the point goal nothing new spawns in the level, but you still have to survive long enough to clear it. Beating a set of levels in the main game unlocks them in gauntlet or trophy mode. In the original Zuma game the regular stuff spawns, progressing from easier fewer colors to more difficult more colors, but there's no time limit, you survive as long as you can trying to get a high score. In Zuma's Revenge instead the playing mode changes because a new type of bonus spawns, and you have three minutes to earn as many points as you can. Plants vs. Zombies, also by popcap, has 3 unlockable bonus modes: Survival Endless (waves or zombies of increasing difficulty as long as you can survive), Vasebreaker Endless (a cool solitaire game where you break unmarked vases at your own pace, but when the vase is broken wither a zombie or a weapon comes out and you have a limited amount of time to deal with it, I'm addicted to this minigame ) and I Zombie Endless (you play the zombies - would be cool but it's not balanced very well). On the other hand I really wished the main game had had a hard mode, because you can replay it but it's so easy after you've earned all the power-ups that it's pointless.

I'm thinking about the Thief games where difficulty would add extra objectives. I've no idea if it also made the enemies harder. It would be things like "get xyz amount of gold", "Don't kill anyone" that kind of thing. A little less than your idea but on a similar theme.

I was thinking about Thief 2 as well! Man that was one hell of a game.

It worked very well for Thief due to a couple of reasons.

1) Combat was, inherently, multi-layered since enemies could be both knocked out and killed. Killing enemies was often easier to do, but caused bloodstains (which could be detected), and a lot more noise than a silent knockout. The bread and butter knockout method was to sneak up behind someone and smack them with a sap, but that took a lot more finesse than shooting some chump in the head with an arrow.

2) Typically speaking, it was dangerous to spend a long amount of time in a level, particularly later ones. Patrols often got pretty dense and harder to sneak through, and juicy treasure was well guarded (but optional!). By imposing the "steal X gold" limit, it forced players to really scour the map and seek out dangerous areas.

This did change how you played the game, but in much more subtle ways than what you're suggesting. It's a cool idea to have the same level, but give the player different ways to play through it. It would place a burdern on level design, though, since you'd need one level design to work with several radically different gameplay approaches.

I believe it can be done, however! Deux Ex did this implicitly, since you could build your character in very different ways. While they didn't tell you, or force you, to be like, "Yo dawg sneak this shit", they provided a ton of different hooks to approaching solutions. If there was a room full of dudes you had to traverse, you could go in guns blazing and kill them all, or you could try to sneak around them, or you could hunt the level and pick the lock on an access vent that bypassed the room, or you could sweet-talk an NPC into causing a distraction, or you could hack into the security system to turn the turrets in the room against the enemy. Stuff like that.

As Acharis alluded to, I think you're confounding two different things: difficulty and play-style. Thing of them as axes that are orthogonal. One really has nothing to do with the other.

I can imagine a player wanting to play a really hard sneaky sniper type game, and I can image a player wanting to play a really easy sneaky sniper type game.

If you flatten these two axes into one, you are going to make a large portion of players unhappy because they can't play how they want to play.

Maybe the difficulty could constrain options. Looking at Splinter Cell games, the lower difficulty levels made enemies less alert and weaker in combat, so you could be forgiven the odd sound or misstep, and even if you did get straight-up spotted, you'd be able to fight your way out of almost any situation, with enough ammo and grenades. Te get through a level undetected, or to kill nobody, was a feat, an optional achievement. As you ramp up the challenge, it not only becomes more difficult to avoid detection, it becomes more important to do so, since you'll have more trouble evading or defeating a pursuer.

That way, the game's difficulty setting forces the player to play at their peak skill level all the time. If you go for top challenge, you can still choose between sneaking and shooting, but if you're sneaking you need to be damned sure you sneak right, and if you're shooting, you've got to use all your tools, with traps and distractions and carefully plotted tactics, or else you're going to get your clock cleaned.