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In the multiferroic phase exhibited by spinel CoCr₂O₄ below T_S = 24K, the two contributing sublattices, Co²⁺ and Cr³⁺, are expected to be strongly coupled. With applied pressure, the coupling between the two sublattices can be enhanced, rendering the possibility of multiferroicity at temperatures higher than T_S. We present a temperature and pressure dependent Raman scattering study of the magnon and phonon spectrum to elucidate the microscopic details of intersublattice interactions and spin-lattice coupling in CoCr₂O₄. At temperatures higher than T_S, with increasing pressure (P > 30kbar), in addition to an existing T_1g magnon at ambient pressure, a second magnon at lower energies is observed, which could indicate increased single-ion anisotropy or spin-spin interactions. We also observe a splitting of the triply degenerate T_2g phonon, possibly indicating spin-induced lowering of crystal symmetry due to increased spin-lattice and intersublattice interactions. We are investigating whether these signatures reflect a multiferroic phase at T>T_S, which would indicate that pressure can be used to tune the coupling between lattice and spin dynamics to control the multiferroic behavior in CoCr₂O₄.