We prefer to keep such commonplace or even clichéd phrases, some of which are listed in hyphenated form in standard dictionaries, open when they appear after the noun they modify or when they are used adverbially:
step-by-step recovery (where “step-by-step” is a phrasal adjective preceding the noun it modifies)
feelings that were out of date (because “out of date” follows the noun it modifies)
walking across the continent step by step (because “step by step” is functioning as a phrasal adverb)
This is a reversal of our recommendation in the fourteenth edition of CMS, which we decided was no longer up to date.
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