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Van der Waals material CuInP₂S₆ (CIPS) exhibits room temperature ferroelectricity with unconventional quadruple-well. Here we report the effect of a ferroelectric substrate on the domain formation and piezoelectric response of CIPS. We mechanically exfoliated 8-250 nm CIPS flakes and transferred them on top of Si, Au, and 50 nm epitaxial (001) PbZr_0.2Ti_0.8O₃ (PZT) films. Piezoresponse force microscopy (PFM) studies show spontaneous domain formation in CIPS flakes on Si and Au substrates, while flakes on PZT exhibit uniform polarization that is fully aligned with the pre-patterned domain structures in the underlying PZT. We also performed in-situ PFM studies at elevated temperatures, which reveals an enhanced Curie temperature of  ~200 ºC for CIPS on PZT. We further extracted the piezoelectric coefficient d₃₃ for these samples. The d₃₃ for thin CIPS on PZT is significantly enhanced compared with those on Au and Si, and changes from 10 pm/V for the 8 nm sample to -8 pm/V for flakes thicker than 25 nm. We attribute this result to the shift of Cu cation from the metastable position to the ground state position in the quadruple-energy-well, which is driven by the interfacial polar coupling with PZT. Our study points to a new strategy to engineering the piezoelectric response of CIPS.