Solvation effects on the geometries and electronic and thermodynamic stabilities of a series of small multiply charged polyatomic anions, which are not electronically and thermodynamically stable in the isolated state, have been studied using the generalized conductor-like screening model of solvation. It was found that small doubly charged anions such as O2-, CO32-, and SO42- are electronically very stable in water with estimated vertical electron detachment energies as high as 6-7 eV. Even the triply charged (BO33-, PO43-, and MgF53-) and quadruply charged (MgF64-) anions are electronically stable in water. In the gas phase MgF42-, MgF53-and MgF64- are not stable toward loss of one F- anion, but the doubly and triply charged anions were found to be thermodynamically stable in water. Surprisingly, the aqueous electron detachment energies are not very strongly dependent on the charge of the anion, and the thermodynamic stabilities of singly, doubly, and triply charged MgF(2+n)(n-) anions are very similar (as a result of which one can expect the coexistence of various charged anions in solutions and in melts).