  We provide a precise geometric picture that demystifies the phenomenon of
supersymmetry enhancement along certain RG flows of four-dimensional field
theories, recently discovered by Maruyoshi and Song. It applies to theories of
arbitrary rank and it is based on a hyperk\"ahler-structure restoration on the
moduli space of solutions of (twisted) Hitchin systems, which underly the
class-S construction we use as an engineering tool. Along the way, we formulate
a necessary algebraic condition for supersymmetry enhancement, and, when
enhancement occurs, we are able to derive the Seiberg-Witten geometry and all
conformal dimensions of Coulomb-branch operators for the infrared theory,
without using a-maximization.
