  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.
