The project cards seem to allow doing this. Is this allowed? Seems overkill since the Empire has such a military advantage. I think most players regard the Death Star as an increasing liability as the game goes on.
Building another whilst you still have the first is definitely allowed.
It isn't overpowered, because if you have two Death Stars, you now have two objective point targets you need to defend from the Rebels.
The only thing you can't have is two Death Stars Under Construction at the same time (only so many construction workers in the galaxy). This is only an issue if you are playing the expansion however.