Hyphens, En Dashes, Em Dashes
Q. Does the Manual defend “on a case-by-case basis” over “case by case”?
A. Yes—we would hyphenate. You can deduce this preference from CMOS 7.87: “Multiple hyphens are usually appropriate for such phrases as an over-the-counter drug or a winner-take-all contest.” Hyphens in such phrases aid readability by helping readers to differentiate a modifier of otherwise indeterminate length from the word or words that it modifies. Postscript: As to whether we would defend “on a case-by-case basis” as a phrase, it’s an established idiom and might be preferred in some instances to the more concise “case by case” on that basis alone (so to speak). (Compare “pets will be permitted on a case-by-case basis” to “pets will be permitted case by case.”) But if you’re considering a shipment of beer, you may need to examine it case by case (literally). It’s best to take a case-by-case approach.