In the task of human mesh recovery (HMR), multi-person scenes are particularly difficult to handle due to the many entities that appear and occlusions between them over time. In particular for video inputs, there is a need to track each entity reliably and consistently. Existing methods rely on pretrained human detection modules, increasing their runtime and limiting the number of tracked entities. We present DETRAM, a unified framework for multi-person HMR and tracking that simultaneously detects, reconstructs, and tracks humans across time, both automatically and via user prompts. DETRAM uses a single transformer decoder with an identity-consistent set of learnable query embeddings that persist across frames: detection queries discover new people, tracking queries maintain pose and shape for existing individuals, and prompt queries follow user-specified identities. Our approach achieves state-of-the-art tracking results on PoseTrack21, 3DPW, BEDLAM, and MuPoTS-3D, and competitive reconstruction accuracy on BEDLAM and 3DPW, while uniquely supporting prompt-based tracking of individuals in multi-person scenes. To our knowledge, this is the first method to unify promptability and multi-person HMR with tracking in an endto-end trainable framework, enabling user-directed human analysis in videos.