  A certain class of neutrino mass models predicts long-lived particles whose
electric charge is four or three times larger than that of protons. Such
particles, if they are light enough, may be produced at the LHC and detected.
We investigate the possibility of observing those long-lived multi-charged
particles with the MoEDAL detector, which is sensitive to long-lived particles
with low velocities ($\beta$) and a large electric charge ($Z$) with $\Theta
\equiv \beta/Z \lesssim 0.15$. We demonstrate that multi-charged scalar
particles with a large $Z$ give three-fold advantage for MoEDAL; reduction of
$\Theta$ due to strong interactions with the detector, and enhancement of the
photon-fusion process, which not only increases the production cross-section
but also lowers the average production velocity, reducing $\Theta$ further. To
demonstrate the performance of MoEDAL on multi-charged long-lived particles,
two concrete neutrino mass models are studied. In the first model, the new
physics sector is non-coloured and contains long-lived particles with electric
charges 2, 3 and 4. A model-independent study finds MoEDAL can expect more than
1 signal event at the HL-LHC ($L = 300$ fb$^{-1}$) if these particles are
lighter than 600, 1100 and 1430 GeV, respectively. These compare with the
current ATLAS limits 650, 780 and 920 GeV for $L = 36$ fb$^{-1}$. The second
model has a coloured new physics sector, which possesses long-lived particles
with electric charges 4/3, 7/3 and 10/3. The corresponding MoEDAL's mass
reaches at the HL-LHC are 1400, 1650 and 1800 GeV, respectively, which compare
with the current CMS limits 1450, 1480 and 1510 GeV for $L = 36$ fb$^{-1}$. In
a model-specific study we explore the parameter space of neutrino mass
generation models and identify the regions that can be probed with MoEDAL at
the end of Run-3 and the High-Luminosity LHC.
