Yes and no.
Setting aside TTY/PTS parts of the conversation...
Yes you can run more then one Xorg instance.
X :1
X :2
X :3
would start 3 new Xorg sessions on display ports 1,2, and 3
You can run damn near any command by setting the DISPLAY variable.
so DISPLAY=:1 xterm
would start xterm on display port 1
Your "default" desktop is display port 0 (:0)
Now for the no part.
Unity is not a great desktop environment. As much as some people like it it really departs from a lot of things that make Linux awesome. One of those things, is that it assumes that it will be only running once. So starting Unity on many display ports usually produces tons of errors as both "environments" fight over settings and such.
KDE used to have the same problem (it still might). XFCE and other "more traditional" desktop environments usually work fine, or at the very least, work as one instance per user logged in.
So yes you can run several GUI sessions at once in different TTY/PTY and access them by pressing CTRL+ALT+F7-F12 (depending on kernel settings).