The symmetry-adapted perturbation theory has been used to compute the three-body nonadditivity of Ar-3 interaction. Several components which had not been considered before have been taken into account. A complete nonadditive potential surface has been fitted to 36 computed points. It is found that all of the dispersion components considered, including the famous Axilrod-Teller-Muto term, are significantly damped at short to intermediate interatomic separations. Functional forms describing this damping are obtained from fits to computed values. It is also seen that the leading intramonomer correlation correction to the dispersion energy cannot be ignored as it typically provides about 15% contribution to this energy. The fourth-order dispersion energy is similarly important at intermediate distances. Both components have not been considered before and appear to be necessary for accurate description of Ar-3 interaction. The nonadditivity of the more complicated exchange energies has been examined through second-order including an analysis of the expansion in powers of the interatomic overlap integrals.