I run docker-compose inside supervisord. Surprisingly it works great, they play well together and I highly recommend it for managing multiple compose projects per machine.

    [program:some-docker-project]
    command=docker-compose up
    directory=/opt/some-docker-project
    ...

    [program:some-other-docker-project]
    command=docker-compose up
    directory=/opt/some-other-docker-project
    ...

This style of setup has served many millions of visitors across dozens of projects in production at our company over the last ~3 years. It's like a poor-mans kubernetes, it handles autorestarting failed projects, we handle ingress with cloudflare argo tunnels in docker, and deployments are easy (just git pull && supervisorctl restart all).