Analyzing complex scenes with Deep Neural Networks is a challenging task, particularly when images contain multiple objects that partially occlude each other. Existing approaches to image analysis mostly process objects independently and do not take into account the relative occlusion of nearby objects. In this paper, we propose a deep network for multi-object instance segmentation that is robust to occlusion and can be trained from bounding box supervision only. Our work builds on Compositional Networks, which learn a generative model of neural feature activations to locate occluders and to classify objects based on their non-occluded prts. We extend their generative model to include multiple objects and introduce a framework for efficient inference in challenging occlusion scenarios. In particular, we obtain feed-forward predictions of the object classes and their instance and occluder segmentations. We introduce an Occlusion Reasoning Module (ORM) that locates erroneous segmentations and estimates the occlusion order to correct them. The improved segmentation masks are, in turn, integrated into the network in a top-down manner to improve the image classification. Our experiments on the KITTI INStance dataset (KINS) and a synthetic occlusion dataset demonstrate the effectiveness and robustness of our model at multi-object instance segmentation under occlusion.