The optimal coordination of primary and backup over-current relays (OCRs) scheme has become one of the main challenges in modern MV-distribution networks (DN) owing to the multi-looped structure and the increased penetration of interment nature-DGs with large-share capacities. The changeable operational topologies of microgrids in modern DN have increased the computational burden to obtain the optimal setting of OCRs. The discrimination time of OCRs scheme may be no longer sufficient or even unmanageable to provide reliable performance in the islanded and grid-connected operational modes. The numerous previously reported optimization techniques employed for OCR coordination may have some limitations/drawbacks regarding OCRs coordination and their framework. Therefore, this study provides a well-defined analytical examination of the limitations in the tripping characteristics of manufactured OCRs. A new constraint taking into consideration maximum plug setting multiplier (PSM) was purposed to improve the optimization techniques. Moreover, enhance the complementary with industrial OCRs tripping characteristics with the optimization techniques in term of coordination time interval. GA in MATLAB had been used to optimize time multiplying setting (TMS) for OCRs coordination. An IEC microgrid benchmark network implemented in ETAP to investigate the effectiveness of the proposed new constraint to enhance the constrained optimization approach in islanded and grid-connected modes.