I have a running Home Assistant Docker container. Now I would like to add Supverisor Docker. Is it possible to separately install Supervisor on docker?
No you cannot
You also cannot have supervised install inside docker
Short answer: no
Long answer: You want to install Home Assistant OS, which takes over the whole computer/virtual machine.
The answers above are not correct - installing an ~orchestrator (eg HA’s Supervisor) as a container itself can be accomplished straightforwardly. It requires exposing the docker sock to the container. This obviously provides effectively near root control of the host (but that’s no different than the surface area of the host-installed supervisor). Note I’m not referring to DinD.
There are some significant benefits to running the entire system - including Supervisor - fully dockerized … but it also adds another layer of complexity, and is not a perfect fit as it breaks encapsulation for non-HA services you have running on the same host. So it is understandable this isn’t a common path.
Personally I’d like to avoid the full overhead and maintanance headache of a full VM, and am likely going to install Supervisor (and a docker instance) under LXD (aka “system” containers)
That’s going to be so far removed from what’s supported that it’s unreal. When things break you’ll be largely on your own.
Please do read the requirements for Supervised before you commit yourself to such an abomination.
Thanks for your reply - if you’re familiar with system containers & have any specifics you envision causing me issues, I’d love to hear it, if you’re correct you’d save me a bunch of time 
exposing /dev to the system container is (hehe) logically identical to exposing it to a vm. an lxc/system container is very similar to a full vm here. Whether to expose host dbus, or specific device nodes, is a little more complicated.
one question I have is for the (supported/official) VM installation - is there a summary somewhere of what host hardware resources the guest OS requires? Both a vm and system-container will run their own init process, dbus, etc. So to the extent the official VM only requires it’s disk & network, system-container and VM are very compatible. host events, and /dev/ nodes can be mapped in explicitly - it gets a lot more detailed in other areas, admittedly only some of which I have direct experience in. But I am not aware of any physical resources the full HA install would require besides network access, and ownership of an fs tree. Does it even require guest-tools installed?