Although it is generally accepted that massive galaxies form in a two-phased fashion, beginning with a rapid mass buildup through intense starburst activities followed by primarily dry mergers that mainly deposit stellar mass at outskirts, the late time stellar mass growth of brightest cluster galaxies (BCGs), the most massive galaxies in the universe, is still not well understood. Several independent measurements have indicated a slower mass growth rate than predictions from theoretical models. We attempt to resolve the discrepancy by measuring the frequency of BCGs with multiple cores, which serve as a proxy of the merger rates in the central region and facilitate a more direct comparison with theoretical predictions. Using 79 BCGs at z=0.06-0.15 with integral field spectroscopic data from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) project, we obtain a multiple-core fraction of 0.11+/-0.04 at z~0.1 within an 18kpc radius from the center, which is comparable to the value of 0.08+/-0.04 derived from mock observations of 218 simulated BCGs from the cosmological hydrodynamical simulation IllustrisTNG. We find that most cores that appear close to the BCGs from imaging data turn out to be physically associated systems. Anchoring on the similarity in the multiple-core frequency between the MaNGA and IllustrisTNG, we discuss the mass growth rate of BCGs over the past 4.5Gyr.