High-energy states of interlayer excitons (IXs) in van der Waals heterostructures remain largely unexplored despite their importance for understanding many-body interactions and nonlinear optical phenomena. Here, we use photoluminescence excitation (PLE) spectroscopy to resolve a Rydberg-like series of excited IX states in MoSe₂/WSe₂ heterostructures. We observe multiple PLE resonances below the intralayer exciton energies, which we assign to the 2s-, 3s-, and 4s-like states of the IXs. These resonances are consistently observed across heterostructures with different twist angles, indicating that the high-energy state spectrum is only weakly affected by the twist angle. Wannier-exciton calculations incorporating screened Coulomb interactions reproduce the overall energy scale and qualitative trends of the measured Rydberg-like series, supporting the assignment of the observed resonances. Our findings demonstrate that PLE provides direct experimental access to the previously unexplored high-energy IX states in van der Waals heterostructures.