Detecting occluded objects still remains a challenge for state-of-the-art object detectors. The objective of this work is to improve the detection for such objects, and thereby improve the overall performance of a modern object detector. To this end we make the following four contributions: (1) We propose a simple 'plugin' module for the detection head of two-stage object detectors to improve the recall of partially occluded objects. The module predicts a tri-layer of segmentation masks for the target object, the occluder and the occludee, and by doing so is able to better predict the mask of the target object. (2) We propose a scalable pipeline for generating training data for the module by using amodal completion of existing object detection and instance segmentation training datasets to establish occlusion relationships. (3) We also establish a COCO evaluation dataset to measure the recall performance of partially occluded and separated objects. (4) We show that the plugin module inserted into a two-stage detector can boost the performance significantly, by only fine-tuning the detection head, and with additional improvements if the entire architecture is fine-tuned. COCO results are reported for Mask R-CNN with Swin-T or Swin-S backbones, and Cascade Mask R-CNN with a Swin-B backbone.