so, how do you handle database reads when you've outgrown simple read replicas?

We've kind of hit a wall with scaling our read replicas. They help, sure, but the main database is still getting hammered when we're super busy. I'm looking into stuff other than just adding more replicas or sharding, which seems like a lot of work. Has anyone actually done things like database connection pooling on a big scale, or maybe caching layers that are even closer to the app, you know, like client-side or distributed memory caches (Redis or Memcached) to take some of the read load off? What were the downsides you ran into with that?