Seven nonlinear optical (NLO) active selenides in the middle IR region, AX(4)(II)X(5)(III)Se(12) (A = K+-Cs+; X-II = Mn2+; Cd2+; X-III = Ga3+, In3+) adopting the KCd4Ga5S12-type structure, have been synthesized by high-temperature solid-state reaction of an elemental mixture with ACl flux. Their three-dimensional network structures are stacked by M9Se24-layers of vertex sharing MSe4 tetrahedra, of which each center is jointly occupied by XII and XIII atoms. Studies suggest that such tetrahedral building units can be regarded as the "multi-functional sites", on which the Cd2+/Ga3+ pair gives rise to the coexistence of NLO and thermochromic properties, and the Mn2+/In3+ pair leads to the coexistence of NLO and magnetic properties. The density functional theory (DFT) studies and the cutoff-energy-dependent NLO coefficient analyses reveal that such "multi-functional sites" contribute to the origin of the second harmonic generation (SHG) that is ascribed to the electronic transitions from the Se-4p states to the ns, np states of X-II and X-III atoms. Remarkably, title compounds show very strong SHG at an incident wavelength of 2.05 mu m, roughly 16-40 times that of commercial AgGaS2; among them, ACd(4)In(5)Se(12) (A = Rb, Cs) represents the strongest SHG among chalcogenides to date.