It is possible, but it is not a wayland limitation per-say but a compositor one (aka the wayland server), and I say "limitation" if the compositor doesn't have multi-display option.

Technically wayland is not the issue:

If you look at your /run/user/[uisd] (uid is probably 1000) you will see the wayland "displays" (socket here), usually named wayland-X. The /run[...] is usually set from $XDG_RUNTIME_DIR while the wayland socket to be used is set in the environment variable $WAYLAND_DISPLAY. So running an application in a 2nd session would just require setting the $WAYLAND_DISPLAY to an other value (that exists).

It seems that Sway is able to do this with the output command.