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Copper indium thiophosphate (CuInP₂S₆) is a van-der-Waals (vdW) layered crystal that is ferrielectric below room temperature. It has unusual properties, including a negative longitudinal piezoelectric coefficient whose atomistic origin remains unknown. In this talk, we present the results of density functional theory calculations which show that the potential energy for Cu displacement away from the centrosymmetric position has two distinct minima in each longitudinal direction instead of the usual one, with stable positions within the layer as well as in the vdW gap. The two minima correspond to two structural phases with distinct polarizations, which is corroborated by piezoresponse force microscopy experimental data. The anharmonicity of the potential governing Cu displacements yields a negative piezoresponse in one of the phases. At the same time, the potential is strongly influenced by strain and the corresponding width of the vdW gap, rendering CuInP₂S₆ a rare example of a uniaxial non-zero-polarization multi-well ferroelectric, with new potential for both fundamental studies and prospective applications.