Can I run Wayland and X11 compositors side by side on one system?

I would like to run a Wayland based comp (KDE Plasma) and an X11 based one (Mate+Xmonad) on the same system. The scenario could be something like having user A with KDE and user B with Mate. A third user C might want xfce and so forth. If I understand it correctly, a greeter / display manager such as lightdm runs on X11, so does this pose a problem in switching users? Note: A and B might be the same system user, but wanting to work with a different comp.