The effects of three-body non-additivities on the most stable structures of Ar_n⁺ (3 < n < 27) clusters have been investigated in an extended diatomics-in-molecules (DIM) approach. Nonadditive interaction terms for both the neutral and the ionic trimer have been included explicitly in the DIM Hamiltonian. Structural rearrangement is observed for a number of cluster sizes due to induced dipole-induced dipole interactions.