It remains a challenge to understand the unconventional mechanisms that cause high-T(C) superconductivity in cuprate superconductors, high-T(C) multiferroicity in CuO, or low-dimensional magnetism in the spin-Peierls transition compounds such as CuGeO(3). A common feature of all these copper oxide compounds (containing Cu(2+) ions) is the presence of large magnetic superexchange interactions J. It is a general strategy to apply chemical and/or physical pressure in order to tune these exotic properties. Here we show theoretically, for the first time, the impact of physical pressure on J on CuO, for which we predict a strong enhancement of the low-dimensionality of the magnetic interactions and the spin-frustration at high-pressures. Such modifications are expected to strongly influence the multiferroic properties of CuO. We finally demonstrate that PBE0 hybrid DFT calculations provide reliable J values for a wide range of copper(II) oxides compounds, i.e. CuGeO(3), BaCu(2)Si(2)O(7), BaCu(2)Ge(2)O(7), and La(2)CuO(4).