Post-sinter　annealing　(PSA)　plays　an　essential　role　on　enhancing　coercivity　of　the　single-main-phase　(SMP)　Nd2Fe14B-based　magnets　due　to　the　formation　of　continuous　Nd-rich　grain　boundary　(GB)　layers　to　decouple　the　adjacent　grains.　Here　we　investigated　the　PSA　effects　on　coercivity　of　the　multi　main-phase　(MMP)　[(Nd,Pr)(0.55)Ce-0.45](30.5)FebalM1.0B1.0　(wt.%)　magnet　prepared　by　sintering　the　mixture　of　Ce-free　and　Ce-containing　2:14:1　powders,　which　has　shown　superior　magnetic　properties　to　the　SMP　one　at　the　same　average　composition.　The　annealing　temperature　dependent　investigation　showed　that　the　coercivity　can　be　enhanced　when　annealing　at　low　temperatures,　but　becomes　even　lower　than　that　of　the　as-sintered　state　when　annealing　at　higher　temperatures,　despite　that　continuous　RE-rich　GB　layers　are　formed　after　annealing.　When　raising　the　annealing　temperature,　the　RE　gradients　within　the　2:14:1　phase　grains　are　reduced　to　reach　the　＂close　to　equilibrium　(or　SMP)＂　state　due　to　the　further　elemental　inter-diffusions　among　the　Ce-lean　and　Ce-rich　2:14:1　grains,　which　weakens　the　magnetic　impedance　effect　among　them.　These　findings　suggest　a　unique　clue　to　enhance　coercivity　of　the　MMP　RE-Fe-B　magnets　by　PSA,　i.e.　the　competitive　contributions　between　the　formation　of　continuous　GB　layers　and　the　gradual　chemical　homogenization　should　be　balanced.　(C)　2017　Acta　Materialia　Inc.　Published　by　Elsevier　Ltd.　All　rights　reserved.