A good way to get a look at boxes (brood or surplus) is to remove and set on end each box and look at the bottom. If you see swarm cells at the bottom, you need to open up the brood nest (by either inserting empty frames or by adding a brood box). This also makes it easy to scrape burr comb.
How about supers? Well, if you're working with bare foundation, you'll want to rotate undrawn frames into the middle of the super, and only add additional boxes once the last one is about 70% drawn. Otherwise, you risk the "chimney effect", where bees draw out the middle few frames in each box. (Also a problem with brood boxes.)
But if you have supers of drawn, empty foundation, the more the merrier. From what I can understand, lots of empty comb will encourage a strong colony to gather more nectar.