Collaborative multi-brain motor imagery is an innovative brain-computer interface (BCI) paradigm that records and decodes brain signals from multiple individuals to collectively complete motor imagery tasks. However, existing decoding methods often rely on techniques such as averaging, concatenating, or cross-brain coupling of data or features, and lack coordination between single-brain and multi-brain decision-making in this context. To address this, we propose a dual-branch electroencephalogram (EEG) decoding method that jointly learns private and shared domain information. The method employs a Siamese network for private common spatial pattern (CSP) learning and a feature-sharing network for shared features, then combines the outputs for classification. Experiments with EEG data demonstrated a 10.27% improvement over the single-brain scenario and a 9% improvement over state-of-the-art methods. This approach effectively integrates private and shared domain learning, advancing collaborative BCI technology.