Spin transition materials are known to exhibit a rich variety of behaviors under several stimuli, among which pressure leads to major changes in their electronic and elastic properties. From an experimental point of view, thermal spin transitions under isotropic pressure showed transformations from (i) hysteretic to continuous transformations where the hysteresis width vanishes beyond some threshold pressure value; this is the conventional case. In several other cases very pathological and unexpected behaviours emerged, like (ii) persistent hysteresis under pressure; (iii) non-uniform behavior of the thermal hysteresis width which first increases with pressure and then decreases and vanishes at higher pressures; (iv) furthermore, double step transitions induced by pressure are also often obtained, where the pressure triggers the appearance of a plateau during the thermal transition, leading to two-step transitions, and finally (v) other non-conventional re-entrant transitions, where the thermal hysteresis vanishes at some pressure and then reappears at higher pressure values are also observed. In the present theoretical study, we investigate this problem with an electro-elastic description of the spin-crossover phenomenon by solving the Hamiltonian using a Monte Carlo technique. The pressure effect is here introduced directly in the lattice parameters, the elastic constants and ligand field energy. By considering spin state-dependent compressibility, we demonstrate that a large panel of experimental observations can be qualitatively described with this model. Among them, we quote (i) the conventional pressure effect decreasing the hysteresis width, (ii) the unconventional cases with pressure causing a non-monotonous behavior of the hysteresis width, (iii) re-entrant, as well as (iv) double step transitions accompanied with various types of spin state self-organization in the plateau regions.