A microscopic approach to the problem of cooperative spin crossover in the [MnL2]NO₃ crystal, which contains Mn^III ions as structural units, is elaborated on, and the main mechanisms governing this effect are revealed. The proposed model also takes into account the splitting of the low-spin ³T₁ (t24) and high-spin ⁵E (t23e) terms by the low-symmetry crystal field. The low-spin → high-spin transition has been considered as a cooperative phenomenon driven by interaction of the electronic shells of the Mn^III ions with the all-around full-symmetric deformation that is extended over the crystal lattice via the acoustic phonon field. The model well explains the observed thermal dependencies of the magnetic susceptibility and the effective magnetic moment.