whens it time to consider a CDN for dynamic content

we've been using our own caching and database read replicas to speed things up, and it's worked pretty well. but i'm wondering when we should start thinking about using a Content Delivery Network (CDN), not just for static stuff, but for dynamic content too. have you guys used CDNs for caching API responses or other dynamic data. what kind of numbers or triggers make you consider it, and what are the usual mistakes people make.