Military bases don't constitute an empire. We have no power over the domestic situations in those countries and many of those bases only exist with the permission of the host nation. Which means if the host nation told us to leave, we would.
That is super-power stuff for the purpose of force projection. One of the things that makes us the most powerful superpower in the history of the world isn't just size of our military or technology or even training, it's that our force projection is unmatched. Maybe the British empire came close, but no other empire in history could fight and win a war on the other side of the world.
I'm trying to think (I have admitted numerous times I am not bright). But, what wars have we 'won' on the opposite side of the world without significant aid from other countries? This is an honest question,,,,I really cannot think of any,,,,but they sure might be out there.