Heavy long-lived multi-charged leptons (MCLs) are predicted by various new physics models. These hypothetical MCLs can form bound states, due to their high electric charges and long life times. In this work, we propose a novel strategy of searching for MCLs through their bound state productions and decays. By utilizing LHC-8 TeV data in searching for resonances in the diphoton channel, we exclude the masses of isospin singlet heavy leptons with electric charge $|q|geq 6$ (in units of electron charge) lower than $sim$1.2 TeV, which are much stronger than the corresponding 8 TeV LHC bounds from analysing the high ionisation and the long time-of-flight of MCLs. By utilising the current 13 TeV LHC diphoton channel measurements the bound can further exclude MCL masses up to $sim$1.6 TeV for $|q|geq 6$. Also, we demonstrate that the conventional LHC limits from searching for MCLs produced via Drell-Yan processes can be enhanced by including the contribution of photon fusion processes.
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