This isn't super helpful, but I have managed to get multi-stage builds with complex dependencies to work by manually unpacking the required .deb archives. It is a huge pain though! Honestly, if you need to do this, it is much easier to just use a Debian base image, and use the standard apt commands to install the dependencies.
However, if you REALLY want a minimal container image, you can do it. My only open source example is an example of installing graphviz on top of a Distroless image. You will need to update the versions and find the required debs yourself though:
Hope this helps!
Evan