  Many existing or proposed intensity-frontier search experiments look for
decay signatures of light long-lived particles (LLPs), highly displaced from
the interaction point, in a distant detector that is well-shielded from SM
background. This approach is, however, limited to new particles with decay
lengths similar to or larger than the baseline of those experiments. In this
study, we discuss how this basic constraint can be overcome in BSM models that
go beyond the simplest scenarios. If more than one light new particle is
present in the model, an additional secondary production of LLPs may take place
right in front of the detector, opening this way a new lifetime regime to be
probed. We illustrate the prospects of such searches in the future experiments
FASER, MATHUSLA and SHiP, for representative models, emphasizing possible
connections to dark matter or an anomalous magnetic moment of muon. We also
analyze additional advantages from employing dedicated neutrino detectors
placed in front of the main decay volume.
