We report ab initio potential energy curves for the interaction of ground state He atoms with the triplet He-2* excimers. Fully converged, unrestricted, open-shell, coupled-cluster method including singles, doubles, and perturbative treatment of triples substitutions (UCCSD(T)) is used to compute the He-2*-He potential energy curves for the a((3)Sigma (u)) and c((3)Sigma (g)) states. The internally contracted multireference configuration interaction method (ICMRCI) is used to compute the potential energy curves for a((3)Sigma (u)), b((3)Pi (g)), d((3)Sigma (u)), e((3)Pi (g)), f((3)Sigma (u)), and f((3)Pi (u)) states. Where they can be compared, at the potential minima, the ICMRCI and UCCSD(T) methods agree to within 1 cm(-1). The method reproduces the diatomic He-2 potential with an accuracy of 0.8 cm(-1). An accuracy of similar to2 cm(-1) is estimated for all reported He-2*-He potentials. Calibrations based on Li-He and H-2-He interactions are consistent with this expectation. Calculations on tetratomics, He-He-2*-He, are carried out to assess the nonadditivity of potentials in various states. At short range, nonadditivity arises from polarization effects, while at long-range its nonadditivity is due to the distortion of the Rydberg electron density by the ground state He atoms. Besides potential energy points, electron density plots are provided.