Multi-person motion prediction is an emerging and intricate task with broad real-world applications. Unlike single person motion prediction, it considers not just the skeleton structures or human trajectories but also the interactions between others. Previous methods use various networks to achieve impressive predictions but often overlook that the joints relations within an individual (intra-relation) and interactions among groups (inter-relation) are distinct types of representations. These methods often lack explicit representation of inter&intra-relations, and inevitably introduce undesired dependencies. To address this issue, we introduce a new collaborative framework for multi-person motion prediction that explicitly modeling these relations:a GCN-based network for intra-relations and a novel reasoning network for inter-relations.Moreover, we propose a novel plug-and-play aggregation module called the Interaction Aggregation Module (IAM), which employs an aggregate-attention mechanism to seamlessly integrate these relations. Experiments indicate that the module can also be applied to other dual-path models. Extensive experiments on the 3DPW, 3DPW-RC, CMU-Mocap, MuPoTS-3D, as well as synthesized datasets Mix1 & Mix2 (9 to 15 persons), demonstrate that our method achieves state-of-the-art performance.