How to append command to docker-compose.yml without override existing?

To do this, you would have to define your own ENTRYPOINT in your docker-compose.yml. Besides building your own Dockerfile, there is no way around this.

As much as I am searching, I cannot find a CMD instruction in this image's Dockerfile, though. So this is probably what's being used.

I'm not familiar with PHP, so I cannot estimate what you would have to change to run a container with your specific needs, but these are the points that you should have a look at.