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Magnetically induced topological transitions of isofrequency surfaces of bulk waves propagating through an unbounded biaxial gyrotropic medium are studied. The medium is constructed from a two-component superlattice composed of magnetized ferrite and semiconductor layers. To derive the constitutive parameters of the gyrotropic medium, a homogenization procedure from the effective medium theory is applied. The study is carried out in the frequency range near the frequency of ferromagnetic resonance, where the magnetic subsystem possesses the properties of natural hyperbolic dispersion. The topological transitions from an open type-I hyperboloid to several intricate hyperbolic-like forms are demonstrated for the extraordinary waves. We reveal how realistic material losses change the form of isofrequency surfaces characterizing hyperbolic dispersion. The obtained results broaden our knowledge on the possible topologies of isofrequency surfaces that can appear in gyrotropic media influenced by an external static magnetic field.