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.