At the moment, the only way to launch multiple Versions into the Overlay Player is to go to the Media App and open a Playlist, then click on the Playlist's composite thumbnail, which plays all Versions linked to that Playlist. We've received feedback that this functionality should be supported elsewhere in Shotgun, such as from a Version page.
Please add your support to this feature request if you'd like to play multiple Versions in the Overlay Player from a Versions or Playlist page.