Could Germany build a four-turret Scharnhorst with eight 15-inch guns?
Short answerYes, but the added size and complexity would turn it into a Bismarck-scale project and erase Scharnhorst's production advantages.
NotesA four-turret Scharnhorst is technically possible, but the extra turret is not an isolated change. The hull must grow, more personnel and support systems are required, and fewer yards can handle construction. The design would lose the smaller, cheaper, and quicker advantages of the three-turret ship. In program terms, Germany would be building something much closer to Bismarck than an enlarged Scharnhorst.