X-ray crystal structures and magnetic properties of an isostructural series of iron(III) Schiff base complexes with the general formula [Fe(L⁵)(NCX)]·Solv (where H₂L⁵ = N,N′-bis(2-hydroxy-naphthylidene)-1,6-diamino-4-azahexane, X = S, Solv = tetrahydrofuran, 1a; X = S, Solv = methanol and 0.5 pyrazine, 1b; X = S, Solv = butanone, 1c; Solv = N,N′-dimethylformamide, X = S (1d) or X = Se (1d′); X = S, Solv = dimethyl sulfoxide, 1e) are reported. In the crystals, the individual [Fe(L⁵)(NCX)] molecules are connected through weak C–H⋯O, C–H⋯π or C–H⋯S non-covalent contacts into 2D supramolecular networks, while the guest-solvent (Solv) molecules are trapped in the cavities between two adjacent layers, which are furthermore stabilized by N–H⋯O hydrogen bonds connecting the Solv oxygen atom with the amine group of the [Fe(L⁵)(NCX)] molecule, with the N⋯O distances varying from 2.921(6) Å (in 1d′) to 3.295(2) Å (in 1a). The magnetic properties of the complexes were tuned by the different Solv molecules and as a result of this, four new spin crossover (SCO) compounds with cooperative spin transitions are reported, which are accompanied by thermal hysteresis in two cases (1d and 1e): 1c, T_1/2 = 84 K; 1d, T_1/2↓ = 232 K, T_1/2↑ = 235 K and 1e, T_1/2↓ = 127 K, T_1/2↑ = 138 K. The role of the N–H⋯O hydrogen bonding in the occurrence and tuning of SCO was also computationally studied using a topological analysis, and also by evaluation of non-covalent interaction (NCI) indexes. Both theoretical approaches showed a clear relationship between the strength of the N–H⋯O hydrogen bonds and T_1/2, as already inferred from X-ray structural and magnetic data.