I think that a lot of the computer's energy is needed to run one video, and
it would be too much for it to run multiple parallel sessions. At least on
most computers. So it's setup as a non-multiple user app. I don't think you
can run multiple windows.
Media player hasn't been able to run multiple versions since about version 7
(I think), but if you only need media playback and not the rest of the stuff
WMP does, then Media Player 6.4 is still installed on your PC. Go to
Start -> Run -> mplayer2 & click OK... This can be configured to run
multiple versions...