Alkali metal cations and halogen anions are well-known components of salts. New classes of molecules referred to as superalkalis and superhalogens exist whose properties resemble those of alkali and halogen atoms, respectively. The former have ionization potentials smaller than those of alkali atoms while the latter have electron affinities larger than those of halogen atoms. Using gradient-corrected density functional theory we have examined the possibility that a new class of salts, referred to as supersalts, could be synthesized with superalkalis and superhalogens as building blocks. The possibility that hyperhalogens can be synthesized by using superalkalis instead of alkali atoms as the core has also been examined. Examples of superalkalis (superhalogens) used in this study include Li3O, Cs2Cl, and Cs2NO3 (BF4, BeF3, and NO3). While supersalts are found to be stable, the ability of superalkalis to form as the core of hyperhalogens is limited due to their large size.