Could a battleship carry four quadruple 16-inch or 18-inch gun turrets?
Short answerIt is theoretically possible, but the ship, construction facilities, dry docks, and support infrastructure would all have to be exceptionally large.
NotesFour quadruple main-battery turrets could be designed, even with 18-inch guns, but the result would be an exceptionally broad and heavy ship. Putting sixteen guns aboard would expand the shipyards, dry docks, maintenance facilities, and amount of metal needed to build and sustain the vessel. A later comparison favors triple turrets because quadruple mounts add another layer of complication. The armament therefore has to be judged together with the naval system that supports it.