2

If one wishes to add "non" in front of a hyphenated adjective, should one add a hyphen after "non?"

1

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
quasi-public–quasi-judicial body
    but
non-English-speaking countries
not-to-be-forgotten moments

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.

2

"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:

non-red-haired [noun]

In this case, it's clear we're negating the entire adjective rather than just the color.

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