  We propose a novel scheme for performing a beam-dump-like experiment with the
general-purpose detectors (ATLAS and CMS) at the LHC. Collisions of high-energy
protons result in jets containing a number of energetic hadrons and
electromagnetic objects that are essentially "dumped" to hadronic and
electromagnetic calorimeters, respectively, and induce the production of
secondary hadrons, electrons, and photons in calorimetric showers. We envision
a situation where new physics particles are produced by the interactions of
these secondary particles inside the calorimeters. For proof of principles, we
consider the axion-like particles (ALPs) produced via the Primakoff process in
the presence of their interaction with photons at CMS. We argue that the drift
tube chambers and the ME0 module of the muon system can serve as detectors to
record the photons from the ALP decay, demonstrating that the resulting
sensitivity reach is competitive due to their close proximity to the signal
source points. We further show that the LHC does not suffer from a barrier,
dubbed beam-dump "ceiling", that typical beam-dump experiments hardly surpass,
carrying the great potential for exploring a wide range of parameter space in
increasing statistics. This analysis can be extended to investigate various
types of light mediators with couplings to the Standard Model leptons and
quarks.
