Multiple sessions of X

Yes, you can. When you issue the first startx command on your system, it opens the first X-session on the default display 0. The second X-session must be opened on a different display. For example, this will open a second X-session on the display 1:

startx -- :1

You can have up to 6 concurrent X sessions. Use <Ctrl><Alt><F7> to switch to display 0, <Ctrl><Alt><F8> to second screen, etc. up to <Ctrl><Alt><F12> Try man startx if you need more info.

In a similar fashion, you can open another bare X-server session without a window manager. This will open one on display 2:

xinit -- :2

On this bare-bone X-display I can run a different windows manager (so as to have two different ones running at the same time) by typing in the X-terminal window one of these (see the previous answer for more details):

startkde

gnome-session

xfce

afterstep

AnotherLevel

fvwm2

fvwm