We use quantum-chemical density functional theory calculations to elucidate the origin of spin-crossover pathways in two iron(II) [2 x 2] molecular grids with carbohydrazide-based bridging ligands. The complexes are characterized energetically and structurally in five available spin states. Special attention is paid to analysis of the structural distortion induced on each iron center by spin transition on any of its neighbors. The evolution of coordination polyhedra is monitored using the Continuous Shape Measures. It is demonstrated that a succession of spin transitions on different centers depends on the character of the induced distortion, either approaching or getting them away from a more regular low-spin geometry. These effects, resulting from the elasticity of bridging ligands, can be modulated by weak perturbations such as a change of the positions of the hydrogen atoms.