Layered metal thio- and selenophosphates (MTPs) are a family of van der Waals gapped materials that exhibit a multitude of functionalities in terms of magnetic, ferroelectric, and optical properties. Despite the recent progress in terms of understanding the material properties of these compounds, the potential of MTPs as a material class yet needs further scrutiny, especially in terms of nonlinear optical properties. Recent reports of efficient low-order harmonic generation and extremely high third-order nonlinear optical properties in MTPs suggest the potential application of these materials in integrated nanophotonics. In this article, we investigate the high-order nonlinear response of bulk and exfoliated thin-film crystals of copper indium thiophosphate (CIPS) to intense mid-infrared fields through experimental and computational studies of high-order harmonic generation (HHG). From a driving laser source with a 3.2 μm wavelength, we generate odd and even harmonics up to the 10th order, exceeding the bandgap of the material. We note conversion efficiencies as high as 10-7 measured for the fifth and seventh harmonics and observe that the harmonic intensities follow a power law scaling with the driving laser intensity, suggesting a perturbative nonlinear optical origin of the observed harmonics for both bulk and thin flakes. Furthermore, first-principles calculations suggest that the generation of the highest harmonic orders results from electron-electron interactions, suggesting a correlation-mediated enhancement of the high-order optical nonlinearity.