Computer animation's quest to bridge content and style has historically been a challenging venture, with previous efforts often leaning toward one at the expense of the other. This paper tackles the inherent challenge of content-style duality, ensuring a harmonious fusion where the core narrative of the content is both preserved and elevated through stylistic enhancements. We propose a novel Multi-condition Motion Latent Diffusion Model (MCM-LDM) for Arbitrary Motion Style Transfer (AMST). Our MCM-LDM significantly emphasizes preserving trajectories, recognizing their fundamental role in defining the essence and fluidity of motion content. Our MCM-LDM's cornerstone lies in its ability first to disentangle and then intricately weave together motion's tripartite components: motion trajectory, motion content, and motion style. The critical insight of MCM-LDM is to embed multiple conditions with distinct priorities. The content channel serves as the primary flow, guiding the overall structure and movement, while the trajectory and style channels act as auxiliary components and synchronize with the primary one dynamically. This mechanism ensures that multi-conditions can seamlessly integrate into the main flow, enhancing the overall animation without overshadowing the core content. Empirical evaluations underscore the model's proficiency in achieving fluid and authentic motion style transfers, setting a new benchmark in the realm of computer animation. Upon its final acceptance, our source codes will be made publicly available.