The CMS in question had 1,800 templates, 14 plug-ins nobody had touched in five years, and a deploy script that included the words "good luck". A big-bang rewrite would have failed, and the editors couldn't go dark for a quarter.
We used the strangler-fig pattern: a thin gateway in front of the monolith, with new content types served from a fresh content service and old ones still served from the legacy CMS. We migrated section-by-section over nine months. Editors saw a single unified editor on day one; readers saw progressively faster pages. On the day we turned the monolith off, no banner went up - because nothing changed for the user.