Large coupling strengths in exciton-photon interactions are important for the quantum photonic network, while strong cavity-quantum dot interactions have been focused on s-shell excitons with small coupling strengths. Here we demonstrate strong interactions between cavities and p-shell excitons with a great enhancement by the in situ wave-function control. The p-shell excitons are demonstrated with much larger wave-function extents and nonlocal interactions beyond the dipole approximation. Then the interaction is tuned from the nonlocal to the local regime by the wave function shrinking, during which the enhancement is obtained. A large coupling strength of 210 μeV has been achieved, indicating the great potential of p-shell excitons for coherent information exchange. Furthermore, we propose a distributed delay model to quantitatively explain the coupling strength variation, revealing the intertwining of excitons and photons beyond the dipole approximation.