  The neutral Higgs boson predicted from spontaneous breaking of electroweak
symmetry in the standard model (SM) has been discovered. Precision test of the
Higgs boson properties is one of the promising ways to study new physics beyond
SM. Some of the most important information to know is whether there are
additional Higgs bosons, neutral, singly charged and even multi-charged ones.
In this work, we study the potential to search for triply charged Higgs bosons
in the final state with at least three same-sign leptons. A detailed collider
analysis of the SM backgrounds and signals at a 100~TeV $pp$ collider is
performed with $5\sigma$ discovery prospects being obtained, which are
expressed as a function of the vacuum expectation value (VEV) $v_\Delta$ or the
mass splitting $\Delta m$. We also revisit the sensitivity at the Large Hadron
Collider (LHC) by projecting that at a 100~TeV $pp$ collider. For a comparison,
two benchmark values $v_\Delta=10^{-6}~\text{GeV}$ and $5\times
10^{-3}~\text{GeV}$ are taken. We find that for the triply charged Higgs boson
mass below 1~TeV $5\sigma$ discovery significance can be reached at a 100~TeV
$pp$ collider with $3.3~\text{fb}^{-1}$ and $110~\text{fb}^{-1}$ of data,
respectively, the sensitivity of which is much better than that at the LHC.
