The transition temperature T c of unconventional superconductivity is often tunable. For a monolayer of FeSe, for example, the sweet spot is uniquely bound to titanium-oxide substrates. By contrast for La 2−x Sr x CuO 4 thin films, such substrates are sub-optimal and the highest T c is instead obtained using LaSrAlO 4 . An outstanding challenge is thus to understand the optimal conditions for superconductivity in thin films: which microscopic parameters drive the change in T c and how can we tune them? Here we demonstrate, by a combination of x-ray absorption and resonant inelastic x-ray scattering spectroscopy, how the Coulomb and magnetic-exchange interaction of La 2 CuO 4 thin films can be enhanced by compressive strain. Our experiments and theoretical calculations establish that the substrate producing the largest T c under doping also generates the largest nearest neighbour hopping integral, Coulomb and magnetic-exchange interaction. We hence suggest optimising the parent Mott state as a strategy for enhancing the superconducting transition temperature in cuprates. © 2019, The Author(s).