The mixed modifier effect (MME) in oxide glasses manifests itself as a non-additive variation in certain properties when one modifier oxide species is substituted by another one at constant total modifier content. However, the structural and topological origins of the MME are still under debate. This study provides new insights into the MME by investigating the effect of isostatic compression on density and hardness of mixed MgO/CaO sodium aluminosilicate glasses. This is done using a specially designed setup allowing isostatic compression of bulk glass samples up to 1 GPa at elevated temperature. A mixed alkaline earth effect is found in the compressibility and relative change of hardness, viz., a local maximum of density as a function of Mg/Ca ratio appears following compression, whereas a local minimum of hardness in the uncompressed glasses nearly disappears after compression. Moreover, the densification of these glasses is found to occur at temperatures much below the glass transition temperature, indicating that a non-viscous mechanism is at play. This is further supported by the fact that density relaxes in a stretched exponential manner upon subsequent annealing at ambient pressure with an exponent of ∼0.62. This is close to the Phillips value of 3/5 for relaxation in three dimensions when both short- and long-range interactions are activated.