Depends on the kind of container. It is not necessarily true that 1 container == 1 process. I run Docker containers with 1000s of processes.
Contrast this to 'operating system containers' which are designed to run an init system, so individual containers are intentionally multiprocess. Many virtual private servers run in containers of this kind, e.g., by OpenVZ.
On that note, how come you've gone with Docker for this rather than something like LXC or OpenVZ, which are ostensibly designed for the large, multiprocess container use case?
I would be very keen to understand why LXC is better than Docker for this. I've also read this kind of "marketing" around so called "operating system containers" but I am still clueless why they are better. Concretely, what are the benefits?