Set in present day we would play low ranking employees in an Organization dedicated to scientific research. Perhaps we could play a Security Guard and a Lab Assistant?
One day our world's are turned upside down when versions of ourselves from ten years in future travel back in time to kill us without warning.
Why are they trying to kill us?
In the future, The Organization creates technology that allows mankind to travel time but the moment they make the discovery they become entangled in a tremendous inter-dimensional war with alternate realities, different versions of themselves all different in some sort of way. (But no crazy mutations.)
The Roleplay would delve deeper into the reason why the alternate realities have to destroy each other. We would succeed in defeating our future selves, by killing them instead. Stranger versions of ourselves would continue to visit our Earth until finally we ourselves discover the secret of time travel and are truly entered into the war.