Once you’ve taken cover, you have that bonus to your defense, the way the taking cover maneuver is worded makes it sound like to me that you either have cover or you don’t. However, while I wouldn’t allow people to take cover twice, I would let them be in cover and drop prone, to get their 2 defense that way.
Another agreement from me. If you are trying to emulate someone getting the most out of their cover, then the prone option behind cover seems to already do that. A second Maneuver to get more cover from the cover you are already behind doesn't make sense. But, I can imagine squatting behind a short wall to get Cover (1 Defense), then going Prone (1 Defense) behind the same wall for a total of 2 Defense.
That being said, game-mechanics-wise, spending extra maneuvers to get extra benefits from cover while not actually being prone should be the purview of a talent, not just something anyone can do. That's how I see it, at least. The trained ship-boarder or trench fighter will know how to get more out of cover than your average guy in a blaster fight.
I wouldn't allow it for a Talent either. What would the Cover Talent emulate? The master at using cover squeezes himself behind the cover and gets more of a bonus? I think anyone knows how to take cover behind an object, experience isn't going to give you some special way to get better cover. There isn't one. I have nearly 20 years in the military and police. I'm currently the team leader of a Special Response Team (aka SWAT). I've yet to discover a "talent" that allows me to take cover behind a tree or corner better then someone else.