Sumo Docker Collectors: is it possible to collect both docker logs & syslogs with the same image?

The Sumo Logic Collector for Docker comes in a few different flavors: a container to collect Docker logs and stats, a syslog collector container, etc.

https://github.com/SumoLogic/sumologic-collector-docker#sumo-logic-collector-for-docker

If I need to collect both Docker logs and syslog logs, would I need to run two of these containers, or is there a way to use the same collector for both? I'm currently running two containers (Docker logs container and syslog container). All of these logs are coming from the same physical host.