The low-lying magnetic excitations in the dimer of single-molecule magnets (Mn4)2 are studied by inelastic neutron scattering as a function of hydrostatic pressure. The anisotropy parameters D and B04, which describe each Mn4 subunit, are essentially pressure independent, while the antiferromagnetic exchange coupling J between the two Mn4 subunits strongly depends on pressure, with an increase of 42% at 17 kbar. Additional pressure dependent powder X-ray measurements allow a structural interpretation of the findings.