Well, you could say it would have been a direct competitor to the Mirage 2000, which is also related to the "mother" Mirage trois.
And what was the case with the F-20, would have been the case with a Mirage III NG
. An old airframe sqweezed to it's limits with these last updates. No room for future upgrades anymore. That's why the F-16 won over the F-20 and probably the Mirage 2000 over the Mirage III NG