The principal aim of the present calculations is to provide highly accurate potential energy surfaces (PES) for the electronic ground state and the first two excited states of the He3+ ion to be employed in subsequent semiempirical modellings of larger helium cluster cations, Hen+. It is well known that the diatomics-in-molecule (DIM) approach, which performs well for the heavier rare gases, fails remarkably even for the smallest Hen+. It is argued that this is mainly due to the neglect of three-body interactions [1] within the DIM framework and, consequently, the three-body contributions to the Hen+ interaction energy have to be extracted from ab initio calculations and included in semiemirical models for them to become acceptably accurate. This can be done, e. g., within the triatomics-in-molecules (TRIM) approach [2], which represents a natural generalization of the DIM method.