The compound {Fe(pmd)[Ag(CN)₂][Ag₂(CN)₃]} (pmd=pyrimidine) was synthesized and characterized. Magnetic, calorimetric and single crystal visible spectroscopic studies demonstrate the occurrence of a two-step high-spin (HS) ↔ low-spin (LS) transition. The critical temperatures are T_c1=185 and T_c2=148 K. Each step involves ~50 % of the iron centers, with the low-temperature step showing a hysteresis of 2.5 K. The enthalpy and entropy variations associated with the two steps are ΔH₁=3.6±0.4 kJ mol^-1 and ΔS₁=19.5±3 J K^-1 mol^-1; ΔH₂=4.8±0.4 kJ mol^-1 and ΔS₂=33.5±3 J K^-1 mol^-1. Photomagnetic and visible spectroscopy experiments show that below 50 K, where the LS state is the thermodynamically stable state, the compound can be switched quantitatively to the HS state using green-red light (550-650 nm). HS-to-LS relaxation experiments in the dark at temperatures between 15 and 55 K show that the relaxation takes place via a two-step cooperative process, which was analyzed in the context of the mean field theory. The crystal structure has been studied at 290, 220, 170, 90 and 30 K together with 30 K after irradiation. The compound adopts monoclinic symmetry (P2₁/c, Z=16) at all temperatures. There are five [FeN₆] pseudo-octahedral sites linked by pmd, [Ag(CN)₂]^- and [Ag₂(CN)₃]^- bridging ligands to form an unprecedented three-dimensional (6,6) topology. The structural analysis allows for an understanding of the microscopic mechanism of the two-step behavior of the thermally induced spin transition as well as the corresponding relaxation of the photoexcited compound based on the individual changes of the five sites. Synergy between metallophilic interactions and the spin transition is also shown by the variation of the Ag^…Ag distances. Correlations between the variation of the unit-cell volume and the change of Ag^…Ag interactions within each step with the asymmetric change of the anomalous heat capacity have also been inferred.