  The neutrino physics program at the LHC, which will soon be initiated by the
FASER experiment, will provide unique opportunities for precision studies of
neutrino interaction vertices at high energies. This will also open up the
possibility to search for beyond the standard model (BSM) particles produced in
such interactions in the specific high-energy neutrino beam-dump experiment. In
this study, we illustrate the prospects for such searches in models with the
dipole or $Z^\prime$ portal to GeV-scale heavy neutral leptons. To this end, we
employ both the standard signature of new physics that consists of a pair of
oppositely-charged tracks appearing in the decay vessel, and the additional
types of searches. These include high-energy photons and single scattered
electrons. We show that such a variety of experimental signatures could
significantly extend the sensitivity reach of the future multi-purpose FASER 2
detector during the High-Luminosity phase of the LHC.
