Out-of-plane polarized ferroelectric materials in a capacitive structure provide a key component for several technological applications. Furthermore, two-dimensional materials are expected to aid in the quest for both ultrathin and flexible electronics. Of the various two-dimensional ferroelectrics with out-of-plane polarization, CuInP2S6 is special in that the Cu atoms are highly mobile and it has been shown to possess both low- and high-polarization states. Using density-functional-theory calculations, we explore the stabilization of the ferroelectric state for several prototypical metal contacts (Gr, Ni, Cu, Au, and Ag). In all cases, we find that the ferroelectric state can be stabilized at fewer layers than in the freestanding case. For all of the considered conventional metal contacts, we also find the existence of a quasi-ferroelectric state that stabilizes a polar phase for thicknesses greater than two layers of CIPS. In the cases of Au and Ag, interfacial alignment and strain can be used to stabilize ferroelectricity at the bilayer limit. Furthermore, we find that the strength of the interaction between the contact and CuInP2S6 also leads to stabilization of the high-polarization state when ferroelectricity is stabilized. Lastly, energy-barrier calculations show that the system is still switchable in the presence of contact doping from the metal contacts.