The crystal structures, phase equilibria and composition ranges of materials that form lithium–manganese spinels have been studied extensively, frequently to optimize specific properties. Here, we report on the Jahn–Teller switching between two tetragonal structures, which is induced by high pressure. Heating the tetragonal phases under high pressure leads to further transformation to the cubic structure. A transformation of the same type was observed upon heating of Li_0.95Mn_2.05O₄ under ambient pressure, however at a milder temperature. The high-pressure high-temperature experiments were performed under pseudo-hydrostatic conditions at pressures of up to 1.87 GPa and temperatures from 303 to 623 K. Furthermore, the axial ratio of tetragonal phases of Li_0.95Mn_2.05O₄ is analyzed. This pressure/temperature switchable material can exhibit a wide range of novel and manipulable properties.