A series of complexes formed between halogen-bonded H(3)N/HCN...BrZ (Z = Br, F) dimers and H(3)N/HCN...BrZ...XY (XY = HF, ClF, BeH(2), LiF) trimers were investigated at the MP2 and B3LYP levels of theory using a 6-31++G(d,p) basis set. Optimized structures, interaction energies, and other properties of interest were obtained. The addition of XY to the H(3)N/HCN...BrZ dyad leads to enhanced intermolecular binding with respect to the isolated monomers. This enhanced binding receives contributions from the electrostatic and inductive forces between the constituent pairs, with, in some instances, substantial three-body non-additive contributions to the binding energy. It was found that the XY = LiF interaction causes the greatest distortion of the H(3)N/HCN...BrZ halogen bond from the preferred linear orientation and also provides the strongest binding energy via the nonadditive energy.