Why the Royal Navy stayed with twin automatic turrets

Did the Royal Navy design triple or quadruple versions of the Tiger-class automatic six-inch turret?

A triple was considered, but the reliable high-rate twin made an extra turret preferable to a heavier three-gun mount.

The Royal Navy considered a triple version of its automatic six-inch mounting but retained the twin. Making a reliable automatic ammunition-handling system becomes harder as more guns share the installation. The Des Moines class showed that a triple eight-inch autoloading mount could work, although the installation was very heavy. The British twin already offered a high rate of fire for the Tiger generation. If more firepower were needed, the preferred use of extra weight would be another complete turret instead of a third gun inside each mounting.