The automation of warehouse operations is crucial for improving productivity and reducing human exposure to hazardous environments. One operation frequently performed in warehouses is bin-packing where items need to be placed into containers, either for delivery to a customer, or for temporary storage in the warehouse. Whilst prior bin-packing works have largely been focused on packing items into empty containers and have adopted collision-free strategies, it is often the case that containers will already be partially filled with items, often in suboptimal arrangements due to transportation about a warehouse. This paper presents a contact-aware packing approach that exploits purposeful interactions with previously placed objects to create free space and enable successful placement of new items. This is achieved by using a contact-based multi-object trajectory optimizer within a model predictive controller, integrated with a physics-aware perception system that estimates object poses even during inevitable occlusions, and a method that suggests physically-feasible locations to place the object inside the container.