Before starting note that this is tested in ubuntu (a debian-based distro).
Here i will be assuming that you are familiar with X-system in linux.
Perhaps you know, what you will get when you press F1 to F8 with control and alt key. Well, if you don't know let me just brief it for you. By default, there are six virtual terminals in linux, F1 through F6.By pressing <ctrl> + <shift> + Fx you can switch to corresponding terminal. Next in F7 there is you your desktop manager. If you are reading this from linux, I must say this is where you currently are. In F8 you will see system logs. From F9 - F12 ...? Yes, this is where we will run other instance of desktop manager.
A brief intro about X-system:
In x-system there are two main parts X-server and X-clients. X-server simply communicates your hardware with the x-clients and a desktop manager gives a gui-environment to make the communication between the user and the x-client easier.
For detail goto wiki-page
Okay, Lets kick off:
It's just a single command. Open a terminal and login using any user-account and just enter the following command:
~$ startx -- :1 &
This command starts a new desktop-manager in screen:1 and the '&' symbol simply backgrounds the process.
The desktop manager on which you currently are, is Screen:0 ==> F7 and by issuing :1 as argument you are requesting to start it on Screen:1 ==> F9 (as you know in F8 there is system log)
Note: You might get it in F8 too or even other in other ditros.
Similarly you can start other three x-client from F10-F12 simply by choosing a from screen 2-4. By starting the x-client as user 'xyz' you will be logged in as same user. And remember you cannot start multiple x-clients in same screen.
In some distro you may also get some error or warning if you try to run it as root.
Note: I have tested it in Ubuntu. If you have tested it successfully in other distro then please post it as a comment.