A poorly understood facet of magnetism concerns its response to the imposition of very high pressures. Here we show that pressure systematically enhances the magnetic properties of titaniferous oxides (titanomagnetite), which are the principal carriers of magnetic remanence in nature. For example, at 4 GPa, saturation remanent magnetization intensities increase by a factor of 2, 3, 13 and 21 for titanomagnetite with 0, 20, 40 and 60% titanium in the structure, respectively. Magnetic coercivity also dramatically rises with pressure for high Ti species. The magnetization intensities and coercivities remain permanently elevated after pressure release. Pressure thus makes multidomain titanomagnetite more single domain-like, which can potentially explain deeply rooted magnetic anomalies on Earth and other planets.