  In pp collisions at LHC energies, heavy quarks are produced in initial hard
scatterings and then these quarks hadronize in either open heavy-flavor hadrons
or quarkonia (e.g. J/$\psi$, $\psi(2S)$, $\Upsilon$). The study of quarkonium
production as a function of charged-particle multiplicity links soft and hard
processes and allows one to study their interplay. While a linear increase of
quarkonium production as a function of charged-particle multiplicity can be
reasonably well understood in the context of multi-parton interactions, the
observation of deviations with respect to a linear increase requires a more
detailed description of the collision. In this contribution, we will present
the latest ALICE measurements at forward rapidity for J/$\psi$ and $\Upsilon$
production as a function of charged-particle multiplicity in pp collisions at
$\sqrt{s}=13$ TeV. The first measurement of the double ratios of relative yield
of $\Upsilon(2S)$ over $\Upsilon(1S)$ and J/$\psi$ over $\Upsilon(1S)$ as a
function of charged-particle multiplicity will also be shown.
