If one wishes to add "non" in front of a hyphenated adjective, should one add a hyphen after "non?"
The Chicago Manual of Style, 14th Edition, addresses this question indirectly in section 5.117:
The en dash is also used in place of a hyphen in a compound adjective when one of the elements of the adjective is an open compound (such as New York) or when two or more of the elements are hyphenated compounds:
New York–London flight
post–Civil War period
Since your usage is of the latter form (a normally hyphenated element in front of a hyphenated compound adjective), the use of multiple hyphens is therefore recommended:
He was the only non-red-haired person in his entire family.
"non" isn't a word, so you can't write this:
non red-haired [noun]
This is less wrong, but I still don't like it:
non-red haired [noun]
We've lost the link between "red" and "haired," so someone might interpret it as "hairy [noun] which is not red."
I like this form:
In this case, it's clear we're negating the entire adjective rather than just the color.