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Entangled coherent states for multiple bosonic modes, also referred to asmultimode cat states, not only are of fundamental interest, but also havepractical applications. The nonclassical correlation among these modes is wellcharacterized by the violation of the Mermin-Klyshko inequality. We here studyMermin-Klyshko inequality violations for such multi-mode entangled states withrotated quantum-number parity operators. Our results show that theMermin-Klyshko signal obtained with these operators can approach the maximalvalue even when the average quantum number in each mode is only 1, and theinequality violation exponentially increases with the number of entangledmodes. The correlations among the rotated parities of the entangled bosonicmodes are in distinct contrast with those among the displaced parities, withwhich a nearly maximal Mermin-Klyshko inequality violation requires the size ofthe cat state to be increased by about 15 times.

Nearly maximal violation of the Mermin-Klyshko inequality with multimode entangled coherent states