If you use the "exploration badge" vendors you can get Mark 2, 5, 6, 8 and 10 green or blue items. As for the vendors in the requisitions area that sell the 'white' mark 1 and 2 items I dont know for sure. There ARE other starbases and some of them do have vendors, but I dont know what exactly they sell.
Comments
Other starbases: K7, Starbase 36, Deep Space Nine.
You should be able to find your Mk II and Mk IV stuff at K7 or Starbase 36.