While containers efficiently implement the idea of operating-system-level application virtualization, they are often insufficient to increase the server utilization to a desirable level. The reason is that in practice many containerized applications experience a limited amount of load while there are few containers with a high load. In such a scenario, the virtual memory management system can become the limiting factor to container density even though the working set of active containers would fit into main memory. In this paper, we describe and evaluate a system for transparently moving memory pages in and out of DRAM and to a NAND Flash medium which is attached through the memory bus. This technique, called Diablo Memory Expansion (DMX), operates on a prediction model and is able to relieve the pressure on the memory system. We present a benchmark for container density and show that even under an overall constant workload, adding additional containers adversely affects performance-critical applications in Docker. When using the DMX technology of the Memory1 system, however, the performance of the critical workload remains stable.