Abstract: In inertial confinement fusion, laser-plasma instability (LPI) is one of the key physical processes affecting experimental performance. The regions where LPI occurs can be divided into single-beam propagation regions and multi-beam overlapping regions. This paper focuses on the multi-beam overlapping region. Based on a general theoretical model of multi-beam LPI, we derive an LPI dispersion relation applicable to arbitrary beam configurations, polarizations, and wavelengths, and develop a corresponding multi-beam LPI dispersion relation code. We apply the theoretical model to experiments on the SG-100kJ facility and the SG-Octopus facility, qualitatively explaining the experimentally observed "intra-cone asymmetry" and "each-beam-goes-home" phenomena. Numerical simulation results reveal that multi-beam effects are present in both phenomena and serve as important factors influencing the development of instabilities. The development of this model and code provides a tool for predicting and controlling multi-beam instabilities in laser fusion facilities.