As mentioned by Jerome,
You also need to add a process manager; for instance Monit or Supervisor. This is because Docker will watch one single process. If you need multiple processes, you need to add one at the top-level to take care of the others. In other words, you're turning a lean and simple container into something much more complicated.
It's not completely clear to me why you would need a process manager inside of a container.
So can someone explain to me, what are all the advantages of having a process manager inside a container? Wouldn't it be better to let systemd or upstart handle the processes, instead of adding extra services to your container?