  We perform a model-independent search for leptoquarks (LQs) at the Large
Hadron Collider through their pair-production and subsequent decay into $t\bar
t \tau\tau$ intermediate states. We show that, assuming full luminosity of the
Run 2, a fully hadronic signal emerging from this intermediate state can
surpass in sensitivity the established searches relying on leptons in the final
state. Our conclusion is supported by a thorough Monte-Carlo analysis, and we
advocate the deployment of our proposed search channel in the proper
experimental setting of the Run 3. Furthermore, in order to highlight the full
scope of this approach for constraining LQ theories, we interpret our results
in the context of the string-inspired Exceptional Supersymmetric Standard
Model, which naturally predicts the $S_1-$type scalar LQ states that we analyse
here.
