When does a multi-layer caching strategy become too much?

So, we're building a new service, and it needs to be fast. Caching, of course, came up right away. We've got the standard setup planned: a CDN for all the static stuff, an in-memory cache on each service for frequently used data, and then Redis for anything that needs to be shared or stick around longer. My feeling is this layered system is good, but I'm worried we might be making it too complicated for some things. Are there times when just one or two layers would be enough, and adding more just creates extra headaches and potential problems with keeping caches in sync? What's the best way to figure out when to simplify?