A series of trinuclear mixed-ligand complexes of iron(II) 2,6-di(pyrazol-1-yl)pyridine moieties with linkers on the basis of 1,3,5-triazapentadiene transition metal (M = Co, Ni, Cu, Zn) bischelates has computationally been designed using the density functional theory TPSSh/6-311++G(d,p) calculations. The systems possessing complete (M = Co, Ni) and partial (M = Cu, Zn) two-step spin-crossover phenomenon at ferrous ions have been revealed. Two spin-state switching mechanisms determining by spin-crossover at iron centers and configurational isomerism at cobalt ion may simultaneously occur in solution of corresponding heterometallic compound (M = Co). The nature of the exchange interactions between paramagnetic metal centers is controlled by variation of a metal in bischelate linker (M = Co, Ni, Cu, Zn). Energy and magnetic characteristics of electromeric forms of the complexes with nickel and copper central metal ions (M = Co, Ni) allow to consider them as promising candidates for the design of molecular switches.