Supervisor: Add hostname mappings to homeassistant docker image config permanently

I’m running HA supervisor and am looking for a supported (preferred) or unsupported method to add host name mappings to the homeassistant docker image config so that the container’s /etc/hosts file is always created with these additional mappings. Ultimately, I want to be able to access devices on my local network through host name aliases from within the container.

I’ve done a lot of searching but I can’t find any documentation on how to do this in a way that preserves the additional mappings after restarting the container. Has anyone else figured this out?