Autonomous vehicles need a complete map of their surroundings to plan and act. This has sparked research into the tasks of 3D occupancy prediction, 3D scene completion, and 3D panoptic scene completion, which predict a dense map of the ego vehicle's surroundings as a voxel grid. Scene completion extends occupancy prediction by predicting occluded regions of the voxel grid, and panoptic scene completion further extends this task by also distinguishing object instances within the same class; both aspects are crucial for path planning and decision-making. However, 3D panoptic scene completion is currently underexplored. This work introduces a novel framework for 3D panoptic scene completion that extends existing 3D semantic scene completion models. We propose an Object Module and Panoptic Module that can easily be integrated with 3D occupancy and scene completion methods presented in the literature. Our approach leverages the available annotations in occupancy benchmarks, allowing individual object shapes to be learned as a differentiable problem. The code is available at https://github.com/nicolamarinello/OffsetOcc .