We investigate how squeezing techniques can improve the measurement precision in multiphase quantum metrology. While these methods are well-studied and effectively used in single-phase estimations, their usage in multiphase situations has yet to be examined. We fill this gap by investigating the mechanism of quantum enhancement in the multiphase scenarios. Our analysis provides theoretical and numerical insights into the optimal condition for achieving the quantum Cramer-Rao bound, helping us understand the potential and mechanism for quantum-enhanced multiphase estimations with squeezing. This research opens up new possibilities for advancements in quantum metrology and sensing technologies.