How much hull would a fourth Scharnhorst turret require?

How much larger would Scharnhorst need to be for a fourth triple 11-inch turret?

Approximately 15-16 metres longer, bringing the hull toward Bismarck's overall length.

The added barbette and machinery demand a longer hull. The approximate length difference between Scharnhorst and Bismarck provides the scale of the change. About 15-16 additional metres would create room for either twelve 11-inch guns or eight 15-inch guns in four turrets. The result is no longer the same compact standardized design and begins to surrender the production advantage at the heart of the scenario.