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The ALICE Collaboration measured three-and four-pion Bose-Einstein correlations(BECs)for Pb-Pb collisions at the Large Hadron Collider(LHC).It is speculated that the observed significant suppression of multi-pi-on BECs is owing to a considerable degree of coherent pion emission in these collisions.Here,we study multi-pion BEC functions for granular sources with coherent pion-emission droplets.We find that the intercepts of the multi-pi-on correlation functions at the relative momenta near zero are sensitive to the number of droplets in the granular source.They decrease with the droplet number.The three-pion correlation functions for evolving granular sources with momentum-dependent partially coherent pion-emission droplets basically agree with the experimental data for Pb-Pb collisions at ysiw = 2.76 TeV at the LHC.However,the model results for the four-pion correlation function are inconsistent with the experimental data.Investigations into normalized multi-pion correlation functions of granu-lar sources suggest an interesting enhancement of the normalized four-pion correlation function in the moderate rel-ative-momentum region.