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A<sc>bstract</sc> We present a detailed study concerning a new physics scenario involving four fermion operators of the Nambu-Jona-Lasinio type characterized by a strong-coupling ultraviolet fixed point where composite particles are formed as bound states of elementary fermions at the scale$$ \Lambda =\mathcal{O}\left(\textrm{TeV}\right) $$ $\Lambda =O\left(\mathrm{TeV}\right)$. After implementing the model in the Universal FeynRules Output format, we focus on the phenomenology of the scalar leptoquarks at the LHC and the High-Luminosity option. Leptoquark particles have undergone extensive scrutiny in the literature and experimental searches, primarily relying on pair production and, more recently, incorporating single, Drell-Yan t-channel, and lepton-induced processes. This study marks, for the first time, the examination of these production modes at varying jet multiplicities. Novel mechanisms emerge, enhancing the total production cross section. A global strategy is devised to capture all final state particles produced in association with leptoquarks or originating from their decay, which we termed “exclusive”, in an analogy to the nomenclature used in nuclear reactions. The assessment of the significance in current and future LHC runs, focusing on the case of a leptoquark coupling to a muon–cquark pair, reveals greater sensitivity compared to ongoing searches. Given this heightened discovery potential, we advocate the incorporation of exclusive leptoquark searches in future investigations at the LHC.