What is the most controlled way to reduce the intensity of orange while keeping its colour family recognisable?

Correct answer: Add a little blue

The governing concept is controlled colour neutralisation. Blue is opposite orange on the colour wheel, so adding a very small amount of blue reduces orange intensity without immediately destroying its hue family. The amount must be measured carefully because excess blue produces a muddy or strongly shifted colour. Much black darkens it, much white creates a tint, and more red increases its warmth rather than reducing intensity.