In recent years, multi-person pose forecasting has gained significant attention due to its potential applications in various fields such as computer vision, robotics, sports analysis, and human-robot interaction. In this paper, we propose a novel deep learning model for multi-person pose forecasting called MPFSIR (multi-person pose forecasting and social interaction recognition) that achieves comparable results with state-of-the-art models, but with up to 30 times fewer parameters. In addition, the model includes a social interaction prediction component to model and predict interactions between individuals. We evaluate our model on three benchmark datasets: 3DPW, CMU-Mocap, and MuPoTS-3D, compare it with state-of-the-art methods, and provide an ablation study to analyze the impact of the different model components. Experimental results show the effectiveness of MPFSIR in accurately predicting future poses and capturing social interactions. Furthermore, we introduce the metric MW-MPJPE to evaluate the performance of pose forecasting, which focuses on motion dynamics. Overall, our results highlight the potential of MPFSIR for predicting the poses of multiple people and understanding social dynamics in complex scenes and in various practical applications, especially where computational resources are limited. The code is available at https://github.com/RomeoSajina/MPFSIR.