In fact, I had started out with the sample Corporate Site, so I should have remembered it was possible.
But in re-designing the layout, the feature has stopped working.
At this point when I try to inherit content from the parent, all the content disappears on that page.
Properties > Template
Inherit content:
Use page template settings [this works for me]
Do not inherit any content
Select inherited levels [all content disappears for me]
Skip Navigation Links.
X Root
X Global Pages
X Offices