Parallels license is for a single computer, so you would have to buy three copies of Parallels. If you wanted to run Windows under Parallels, you'd also have to buy three copies of Windows. You could, of course, run three copies of Linux, or 40 copies of Linux, for free.
I had a similar situation. You need to purchase three programs -- three sets of Parallels. You might "get away" with bootlegging one purchase, but that is theft just as certainly as if you held Parallels up at gunpoint and demanded a copy of their program for free.