  The availability at the LHC of the largest collision energy in pp collisions
allows a significant advance in the measurement of $J/\psi$ production as
function of event multiplicity. The interesting relative increase observed with
data at the LHC at $\sqrt{s} = 7\,\mathrm{TeV}$ and at RHIC at $\sqrt{s} =
0.2\,\mathrm{TeV}$ is studied now at unprecedented multiplicities at $\sqrt{s}
= 13\,\mathrm{TeV}$. The measurement at mid-rapidity in the dielectron channel
with ALICE is presented and discussed in comparison to predictions from
available theoretical models and to data at lower energies.
