american english - Non in front of hyphenated adjective

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

Answer

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.