Our experimental investigation of the quasi-binary systems TixV1-xSn2, TixFe1-xSn2, VxFe1-xSn2, FexCo1-xSn2, and CoxNi1-xSn2 revealed the interesting sequence of structures CuMg2 --> NiMg2 --> CuAl2 --> CoGe2, where the stability is primarily determined by the valence electron concentration (VEC, number of valence electrons per formula unit). In the range between 12.4 and 14.0 electrons per formula unit, the CuMg2 type has been found to be stable, followed by the NiMg2 type in the region between 13.9 and 14.7 and the CuAl2 type in the region between between 14.7 and 17.1 electrons per formula unit. The three structure types are closely related and represent different stacking sequences of layers consisting of square antiprisms formed by the Sn atoms. The structures of Ti0.62V0.38Sn2 (CuMg2 type) Ti0.4Fe0.6Sn2 (NiMg2 type), V0.75Fe0.25Sn2 (NiMg2 type), and V0.72Co0.28Sn2 (NiMg2 type) were determined by single-crystal X-ray diffraction methods. The structural sequence is completed by the CoGe2 structure type in the system CoxNi1-xSn2 when VEC is in the region between 17.2 and 17.6 electrons per formula unit. The theoretical investigation of the systems CrxMn1-xSn2 and CoxNi1-xSn2 by the full-potential linear muffin tin orbital method, combined with the virtual crystal approximation for modeling random occupational disorder of the transition metal atoms, fitted the experimental findings, although the energy differences of the structures CuMg2, NiMg2, and CuAl2 turned out to be very small (less than 0.005 eV/atom in CrxMn1-xSn2). The key role of VEC, that is the band filling, in structural stability for the systems under consideration was confirmed, and the variation of the bonding situation as a function of the band filling was studied by charge density calculations.