The problem with multiple endings, as someone else noted, is that they're a cop-out. There's a bad ending, sure, but there's also a good ending. You have a choice. Victory is an option.
And lots of endings can be downers but still give the player a sense of triumph, of having nobly sacrificed this to accomplish that. The end of Diablo, for instance (hi, Root) was hardly upbeat but, without considering the sequel, the player ends up sacrificing his own happiness and life to contain the great evil and save the village and, presumably, the world. Not great for the player but all in all, a job well done!
But what if somebody made an FPS based on, say, the James Coburn classic Cross of Iron? You play the commander of a squad of German soldiers on the Eastern front, trapped behind enemy lines. You can't count on a rescue because a scheming officer is responsible for putting you there in the first place and regardless, the war is going badly and your comrades are falling back. So it's a desperate fight for survival as you fight your way back to your lines. You struggle to bring your loyal men home but one by one, they're cut down by the enemy, and when you finally catch up with the retreating German forces, the few men still with you are accidentally killed by friendly fire. The End!
(The epilogue will detail how your homeland was razed to the ground by Russian and Allied forces but that you, as the game character, probably won't know that because you were almost certainly killed at some point relative soon after the game ended. There will be no sequel.)
How would that fly?