So, the game I have in mind is a hero shooter, so either totally or mostly multiplayer, so really the premise is more important than a rigidly determined story.
But what I had an idea for is a fairly near-future game where mankind has started to try and expand outside our solar system, but after a series of high-profile accidents, the decision was made that national space agencies (such as NASA), were not to attempt to explore uncharted planets with manned missions. So, to fill the gap, a legal grey area was exploited (and supported by governments) to have privately owned companies send specialists (taken from prisons, the military, etc) down to chart the planets so manned missions are legal.
However, there's competition between the companies, and often they have subordinate goals to just having specialists explore the planets, so they come into conflict with each other. And out there in space, the law's a lot less enforceable