Ga₂O₃ has attracted great attention as a promising material for high power electronic devices due to a very large band gap and high breakdown voltage, with high Baliga’s figure of merit. Ga₂O₃ can be easily doped n-type, with Si, Ge, or Sn as shallow donors, but difficult to dope p-type. All tested candidate acceptor impurities lead to deep acceptor levels, lying at ~1 eV above the valence band. These deep acceptors are still useful for making Ga₂O₃ semi-insulating, adding flexibility to device design, and the interactions between acceptors, such as nitrogen, and donors may play important role in making Ga₂O₃ semi-insulating. Using electronic structure calculations based on hybrid density functional theory, we investigate the interactions between acceptor and donor impurities in different possible configurations of acceptor-donor complexes considering all the inequivalent cation and anion sites of the β-Ga₂O₃ crystal structure. We calculate binding energies of the complexes, and discuss changes in transition levels compared to those of the isolated species. These results aim at facilitating the experimental characterization of acceptor impurities to further the development of Ga₂O₃-based electronic devices.