Formation of the (MgCoNiCuZn)O entropy-stabilized oxide and of the related 4-cation derivatives is achieved using a Pechini route based on cation chelation and subsequent immobilization in a polymer gel. Calcination of the as-obtained resins yields a phase separation into fine-grained oxide precursors, but the extent of this phase separation depends on the formulation. In particular, absence of copper leads to the formation of a multi-element oxide with a rock-salt structure including most of the cations except for Zn at a temperature as low as 450 °C. Starting from these charred resins, the temperature-composition phase diagram of the equimolar mixtures is investigated by in situ powder X-ray diffraction. This study highlights the specific role of copper, with an onset of phase transformation into a phase-pure (MgCoNiZn)O mixed oxide at a temperature 25 °C lower than the one found for the 5-cation reference. Removal of the magnesium and nickel elements has also a pronounced impact on phase stability and lattice distortions after quenching, suggesting a description in terms of site percolation within a (MgNi)O templating network. The optical, dielectric and magnetic properties of the 4-cation compositions with respect to the 5-element high-entropy oxide are discussed in relation with the structural distortions induced at the local scale by the Jahn–Teller Cu2+ ions and at longer range through the destabilization of the rock-salt cubic structure.