The old theory can be changed so far it is not recognizable. Adopting Hamiltonian mechanics or Gaussian coordinates will do that. However, since any such permutation will have to provide the same results that we see in daily life, in addition to new results, it may be said that the old theory has merely been extended in any and all cases.
Yup, that sounds about right, except that usually you should still be able to see the core idea of the original theory under layers of extension and new notation. Newton wouldn't recognize the way we use his laws of motion nowadays (and if he did, he'd be pissed because we all use his old enemy Leibniz's notation for doing calculus), but the new formulas are all derived from his basic ideas.