The Tc of superconducting Y₂Ba₄Cu₇O₁₅.₃₂ is measured up to a pressure of 33.7 GPa. After an initial increase from 95 K to 101.7 K a decrease down to 26.6 K is found, with a clear kink at 22 GPa. We demonstrate that Y₂Ba₄Cu₇O₁₅.₃₂ behaves as a multilayer of YBa₂Cu₃O₇ and YBa₂Cu₄O₈ building blocks coupled via the proximity effect. These data are not consistent with the idea that the coupling of two adjacent CuO₂ planes is necessary for superconductivity.