Resolving real-world human-object interactions in images is a many-to-many challenge, in which disentangling fine-grained concurrent physical contact is particularly difficult. Existing semantic contact estimation methods are either limited to single-human settings or require object geometries (e.g., meshes) in addition to the input image. Current state-of-the-art leverages powerful VLM for category-level semantics but struggles with multi-human scenarios and scales poorly in inference. We introduce Pi-HOC, a single-pass, instance-aware framework for dense 3D semantic contact prediction of all human-object pairs. Pi-HOC detects instances, creates dedicated human-object (HO) tokens for each pair, and refines them using an InteractionFormer. A SAM-based decoder then predicts dense contact on SMPL human meshes for each human-object pair. On the MMHOI and DAMON datasets, Pi-HOC significantly improves accuracy and localization over state-of-the-art methods while achieving 20x higher throughput. We further demonstrate that predicted contacts improve SAM-3D image-to-mesh reconstruction via a test-time optimization algorithm and enable referential contact prediction from language queries without additional training.