In this manuscript we report high level ab initio calculations (RI-MP2(full)/6-31++G**) and experimental evidence that demonstrate that important non-additivity effects between three noteworthy non-covalent interactions that involve aromatic rings (benzene and hexafluorobenzene), i.e. cation-pi, anion-pi and pi-pi interactions, occur when the interactions coexist in the same complex. In some cases we have observed very high non-additivity energies (up to -20.3 kcal mol^-1) that indicate that the cation- and/or the anion- have a strong influence on the – interaction and vice versa.