At the LHC collision energies, multiple parton interactions (MPI) are a key ingredient for particle production models including hard scale processes like heavy-quark production (charm and beauty). Quarkonium measurements in high-multiplicity proton-proton (pp) collisions can shed light on the role of MPI at such hard momentum scales, as well as on the interplay between hard and soft particle production mechanisms. In addition, quarkonium production measurements in minimum bias pp collisions, besides serving as a reference
for heavy-ion collisions collected at the same center-of-mass energy, represent a benchmark test of various QCD based models.
In this contribution, the latest quarkonium measurements performed by the ALICE collaboration in pp collisions at several center-of-mass energies are presented. A comprehensive study of the multiplicity dependence of the quarkonium production at $\sqrt{s} = 13$ TeV, based on minimum bias and high-multiplicity triggered events, is also presented. Such measurements include $\psi$(2S) production at forward rapidity as a function of the charged particle multiplicity density, as well as the latest multiplicity dependent inclusive J/$\psi$ production measurements at midrapidity, based on multiplicity estimators covering different pseudorapidity regions. Similar multiplicity dependent measurements in p-Pb collisions at center-of-mass energies of $\sqrt{s_{\rm NN}} =$ 5.02 and 8.16 TeV are also presented. The reported results are compared with available theoretical model calculations.