Is it possible to upgrade old Mirage-III and Mirage-V variants with thrust-vectoring engines so that they can match the maneuverability of F-16s?
Given enough tinkering, it is technically possible. But so many other modifications would be needed - strengthening, wing revisions to maintain the relationship between centers of lift and gravity, trim authority, managing the changes in stability, never mind the engine mounting and avionics refit, etc. etc. that really you would just be cannibalizing an old airframe to make an entirely new plane.
Somebody might conceivably do it as a short-life proof-of-concept prototype, if a new plane were proposed, the Mirage airframe was a good enough match, and a sophisticated digital control system was not necessary for these early tests. But in practice there is nobody in the world with all of the need, the industrial capability, the Mirages and the budget to embark on a new fighter programme that would require such a prototype.
Dassault did experiment with adding separate lift engines in the fuselage, in the Balzac V (which was just such a hacked-about Mirage III airframe) and the Mirage IIIV (which was twice the size), but it all went nowhere.