It's likely that even neutral governments and powers in the galaxy were in some form of another working alongside the empire either through bribes, blackmail, conquest or threat of conquest.
A combination of diplomacy and more sinister means, aye. Palpatine surely wanted to have it all, but on the other hand an Empire needs to have enemies or other outside threats to deal with. Manipulating the strongest neutral powers through diplomacy and covert actions could well be worth more than going in and conquering them. Make some neutrals feel pressed enough that they take to attacking Imperial shipping, then get good reputation for the Imperial Fleet that protects trade routes from "unknown raiders and pirates". Secretly present the neutrals with proof of their piracy operations and blackmail them on some other issue.
It would make Palpatine feel like the spider in the web, pulling the strands to make the whole galaxy dance to his smallest whims.