The theoretical exploration of the super-chalcogen properties of multi-charged sandwich structures whose geometry simultaneously satisfyies the octet rule and Hückel's 4n+2 rule is reported here via a case study of dianion clusters [M(B2C4X6)2]2- (M = Be, Mg or Ca; X = H, F or Cl). The properties of these dianion clusters [M(B2C4X6)2]2- are close to or even superior to those of traditional clusters based on separate electron-counting rules, i.e., the octet rule and Hückel's 4n+2 rule. At the theoretical level of combined ab initio and DFT methods, these clusters, including halogen-substituents (F, Cl) are super-chalcogens due to their high first vertical electron detachment energy (FVDE), of which the largest value is 1.64 eV. This may be attributed to the strong ability of halogen-substituents (F, Cl) to attract an extra electron, according to an analysis of the distribution of the extra electron, and the spin density and the contribution of HOMO orbitals, leading to a larger spatial extent of the extra electron on both the ring skeleton and halogen ligands, which will lower the electronic kinetic energy according to fundamental quantum mechanics.