The influence of hypothetical new interactions beyond the Standard Model on atomic spectra has attracted recent interest. In the present work, interelectronic photon-exchange corrections and radiative quantum electrodynamic corrections to the hypothetical contribution to the energy levels of few-electron ions from a new interaction are calculated. The 1s, 2s and 2p 1/2 ground states of H-like, Li-like and B-like ions are considered, as motivated by proposals to use isotope shift spectroscopy of few-electron ions in order to set stringent constraints on hypothetical new interactions. It is shown that, for light Li-like and B-like ions, photon-exchange corrections are comparable to or even larger, by up to several orders of magnitude, than the leading one-electron contribution from the new interaction, when the latter is mediated by heavy bosons.