To enhance the convergence efficiency and solution precision of the Red-billed Blue Magpie Optimizer (RBMO), this study proposes a Multi-Strategy Enhanced Red-billed Blue Magpie Optimizer (MRBMO). The principal methodological innovations encompass three aspects: (1) Development of a novel dynamic boundary constraint handling mechanism that strengthens algorithmic exploration capabilities through adaptive regression strategy adjustment for boundary-transgressing particles; (2) Incorporation of an elite guidance strategy during the predation phase, establishing a guided search framework that integrates historical individual optimal information while employing a Lévy Flight strategy to modulate search step sizes, thereby achieving effective balance between global exploration and local exploitation capabilities; (3) Comprehensive experimental evaluations conducted on the CEC2017 and CEC2022 benchmark test suites demonstrate that MRBMO significantly outperforms classical enhanced algorithms and exhibits competitive performance against state-of-the-art optimizers across 41 standardized test functions. The practical efficacy of the algorithm is further validated through successful applications to four classical engineering design problems, confirming its robust problem-solving capabilities.