If you are looking at running a local nested X session, you can simply run:
...to open up a second nested session.
If you want to run a remote nested session, it gets a little more complicated. On the remote host, create the file /usr/local/bin/nestedX with the following content:
...and make the file executable. Then from the guest system:
(Note: ensure that openssh-server is installed and properly configured and that port 22 is allowed through the firewall).
ssh -XfC account-name@my-computer nestedX
dm-tool (part of lightdm) seems tailored to this but I can't seem to find much in the way of documentation. Passing it --help shows some info:
The one thing I haven't been able to figure out is how to change the viewable screen dimensions of the nested session.
$ dm-tool --help
dm-tool [OPTION...] COMMAND [ARGS...] - Display Manager tool
-h, --help Show help options
-v, --version Show release version
--session-bus Use session D-Bus
switch-to-greeter Switch to the greeter
switch-to-user USERNAME [SESSION] Switch to a user session
switch-to-guest [SESSION] Switch to a guest session
lock Lock the current seat
list-seats List the active seats
add-nested-seat Start a nested display
add-local-x-seat DISPLAY_NUMBER Add a local X seat
add-seat TYPE [NAME=VALUE...] Add a dynamic seat