Maximum Inner Product Search (MIPS) is a fundamental challenge in machine learning and information retrieval, particularly in high-dimensional data applications. Existing approaches to MIPS either rely solely on Inner Product (IP) similarity, which faces issues with local optima and redundant computations, or reduce the MIPS problem to the Nearest Neighbor Search under the Euclidean metric via space projection, leading to topology destruction and information loss. Despite the divergence of the two paradigms, we argue that there is no inherent binary opposition between IP and Euclidean metrics. By stitching IP and Euclidean in the design of indexing and search algorithms, we can significantly enhance MIPS performance. Specifically, this paper explores the theoretical and empirical connections between these two metrics from the MIPS perspective. Our investigation, grounded in graph-based search, reveals that different indexing and search strategies offer distinct advantages for MIPS, depending on the underlying data topology. Building on these insights, we introduce a novel graph-based index called Metric-Amphibious Graph (MAG) and a corresponding search algorithm, Adaptive Navigation with Metric Switch (ANMS). To facilitate parameter tuning for optimal performance, we identify three statistical indicators that capture essential data topology properties and correlate strongly with parameter tuning. Extensive experiments on 12 real-world datasets demonstrate that MAG outperforms existing state-of-the-art methods, achieving up to 4x search speedup while maintaining adaptability and scalability.