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Multi-object tracking (MOT) and trajectory prediction are two critical components in modern 3D perception systems that require accurate modeling of multi-agent interaction. We hypothesize that it is beneficial to unify both tasks under one framework in order to learn a shared feature representation of agent interaction. Furthermore, instead of performing tracking and prediction sequentially which can propagate errors from tracking to prediction, we propose a parallelized framework to mitigate the issue. Also, our parallel track-forecast framework incorporates two additional novel computational units. First, we use a feature interaction technique by introducing Graph Neural Networks (GNNs) to capture the way in which agents interact with one another. The GNN is able to improve discriminative feature learning for MOT association and provide socially-aware contexts for trajectory prediction. Second, we use a diversity sampling function to improve the quality and diversity of our forecasted trajectories. The learned sampling function is trained to efficiently extract a variety of outcomes from a generative trajectory distribution and helps avoid the problem of generating duplicate trajectory samples. We evaluate on KITTI and nuScenes datasets showing that our method with socially-aware feature learning and diversity sampling achieves new state-of-the-art performance on 3D MOT and trajectory prediction. Project website is: https://www.xinshuoweng.com/projects/PTP