On our CI server, I setup an apt-cache container, and have a 'base' image derived from bitnami/minideb that sets the container's apt proxy to apt-cache. There's also Squid for HTTP caching, Archiva for Java artifacts, and Devpi for Python ones. So, sure, changes will require re-downloads, but they're pretty fast since everything's local. For getting multi-stage builds to work nicely, I just use a Makefile, defining separate targets for 'builder' images and 'runtime ones', and COPY artifacts from the former into the latter to form the final application images.