Frustrated magnets provide a promising avenue for realizing exotic quantum states of matter, such as spin liquids and spin ice or complex spin molecules. Under an external magnetic field, frustrated magnets can exhibit fractional magnetization plateaus with spin patterns stabilized by field-induced lattice distortions. Magnetization and ultrasound experiments in MnCr2S4 spinel up to 60 T reveal an extremely robust magnetization plateau with an unusual spin structure and two intermediate phases, indicating realizations of supersolid phases. The magnetization plateau characterizes fully polarized chromium moments, without any contributions from manganese spins. At 40 T, the middle of the plateau, a regime evolves, where sound waves propagate almost without dissipation. The external magnetic field exactly compensates the Cr–Mn exchange field and decouples Mn and Cr sublattices. In analogy to predictions of quantum lattice-gas models, the changes of the spin order of the manganese ions at the phase boundaries of the magnetization plateau are interpreted as transitions to supersolid phases in addition to superfluid and crystalline phases (see Ref. [1]). This direct comparison with theory is possible because the effective field at the manganese site can be tuned from plus to minus values. The appearance of an additional phase close to 40 T (that is, effective zero field) results from the complexity of A-site spinels in moderate fields. The present study of exotic phases in MnCr2S4 tuned by high fields offers a versatile ground for realizing novel properties in frustrated magnets.