We use quantum-chemical (DFT) calculations to elucidate the origin of spin-crossover pathways in the iron [2×2] molecular grid with pyrazole-based bridging ligands displaying spin-state and oxidation-state multistability. The complex is characterized energetically and structurally in different available spin and oxidation states. Special attention is paid to the analysis of the structural distortion induced on each iron center by spin transition on any of its neighbors or by oxidation. The evolution of coordination polyhedra is monitored by using continuous shape measures. It is demonstrated that a succession of spin transitions on different centers depends on whether the induced distortion approaches or moves the coordination core geometry away from a more regular low-spin geometry. These effects, as well as the overall grid geometry, are driven by the steric strain in the ligands. We also calculate the parameters of Mössbauer spectra and exchange coupling constants for different grid states.