The many-body symmetry-adapted perturbation theory of intermolecular interactions has been extended to the interactions of three closed-shell atoms or molecules. Orbital formulas for the nonadditivity of the second- and third-order induction energies, thirst-order induction-dispersion energy, and third- and fourth-order dispersion energies with neglect of intramonomer correlation effects have been derived from the polarization expansion, The first-order intramonomer correlation correction to the third-order dispersion energy has also been obtained. The symmetrized Rayleigh-Schrodinger energy expansion has been used to derive orbital formulas for the first- and second-order exchange energies with neglect of intramonomer correlation effects. The first-order exchange energy was approximated by the terms proportional up to the fourth power in the intermolecular overlap integrals. The second-order exchange energy was developed through the third pouter of the intermolecular overlap integrals.