One of the main goals of NA61/SHINE, a fixed-target experiment at the CERN SPS, is the search for the critical point of strongly interacting matter. The comprehensive data collected during a two-dimensional scan in beam momentum (13$A$-150$A$ GeV/$c$) and system size (p+p, p+Pb, Be+Be,
Ar+Sc, Xe+La, Pb+Pb) allows, in particular, for a systematic search for an enhancement of fluctuations of various observables. An example of such observable is local fluctuation of particle densities in transverse momentum space, which can be probed with an intermittency analysis by measuring the scaling behavior of factorial moments of multiplicity distributions.

This contribution reviews the ongoing NA61/SHINE studies of scaled factorial moments of proton multiplicity distributions. New results were obtained for Ar+Sc at 150$A$ GeV/$c$ ($\sqrt{s_{NN}} \approx$ 17 GeV) and Pb+Pb at 30$A$ GeV/$c$ ($\sqrt{s_{NN}} \approx$ 7.5 GeV) collisions, employing a novel approach using cumulative quantities and independent data points are presented.