Accurate segmentation of coronary arteries is a pivotal process in assessing cardiovascular diseases. However, the intricate structure of the cardiovascular system presents significant challenges for automatic segmentation, especially when utilizing methodologies like the SYNTAX Score, which relies extensively on detailed structural information for precise risk stratification. To address these difficulties and cater to this need, we present MPSeg, an innovative multi-phase strategy designed for coronary artery segmentation. Our approach specifically accommodates these structural complexities and adheres to the principles of the SYNTAX Score. Initially, our method segregates vessels into two categories based on their unique morphological characteristics: Left Coronary Artery (LCA) and Right Coronary Artery (RCA). Specialized ensemble models are then deployed for each category to execute the challenging segmentation task. Due to LCA's higher complexity over RCA, a refinement model is utilized to scrutinize and correct initial class predictions on segmented areas. Notably, our approach demonstrated exceptional effectiveness when evaluated in the Automatic Region-based Coronary Artery Disease diagnostics using x-ray angiography imagEs (ARCADE) Segmentation Detection Algorithm challenge at MICCAI 2023.