The coexistence mechanism of species stands as a profound enigma within the realm of community ecology. Traditional coexistence theories, which have long centered on direct interactions between pairs of species, have not always stood the test of time when applied to the complex tapestry of real-world ecosystems. Recent research has heralded the emergence of higher-order interactions, a paradigm that introduces an intricate layer of complexity to the ecological stage, where a species' direct impact on another species is intertwined with the intricate web of indirect influences stemming from the actions of other species. It is within this intricate dance of competition and survival that the structure and dynamics of biological communities take shape. Contemporary explorations into the role of higher-order interactions have primarily unfolded within the theoretical domain, specifically within non-spatial theoretical models. While these models offer valuable insights into the abstract interactions that underpin complex ecological relationships, they often fall short in capturing the full richness and complexity of real-world ecosystems. In stark contrast, real ecosystems are characterized by the spatial distribution of individuals and patterns of dispersal that hold a profound influence over population dynamics. Recognizing the significance of these spatial realities, this study takes a bold step towards bridging the gap between theory and reality. Using three species as its focal point, the study constructs an intricate and spatially explicit model to simulate community dynamics. The central question that underpins this ambitious endeavor is: how do higher-order interactions shape the coexistence of species within the framework of spatial dynamics? The findings of this rigorous exploration unveil several pivotal insights: (1) Higher-order interactions wield the power to either bolster or thwart species coexistence, with specific outcomes intricately entwined with the direction, strength, and classification of these multifaceted interactions. (2) In scenarios where all higher-order interactions are present with positive values, the spatial distribution of species undergoes transformation. Regions where species once coexisted due to niche differentiation may experience shifts in their coexistence dynamics. In areas characterized by a high degree of niche overlap, species may persist across a broader spectrum of fitness differences. (3) The dispersal patterns of species introduce a layer of complexity into the regulatory mechanisms of higher-order interactions. Whether these interactions manifest as positive or negative, their effects tend to diminish when populations exhibit a preference for localized dispersal. In conclusion, these profound findings underscore the critical significance of incorporating interaction networks into both theoretical models and practical conservation endeavors. Such insights not only deepen our comprehension of coexistence mechanisms but also provide valuable theoretical underpinnings for the conservation of biodiversity.