Why battleship anti-aircraft guns cannot fill every open deck

How much more light anti-aircraft armament could a very large battleship carry?

Probably not much more without redesign, because ammunition supply, maintenance, blast effects, and superstructure space constrain the layout.

The answer rejects the idea that every open patch of deck can accept another mounting. Each position needs an ammunition route that can sustain rapid fire and enough access for servicing. Main and secondary batteries also create blast zones dangerous to exposed crews and equipment. Because the superstructure does not expand in proportion to the hypothetical battleship, its usable AA positions remain much more limited than displacement alone suggests.