The implementation of the Multiple Independent Levels of Security (MILS) software architecture on modern microprocessor architectures has become technically feasible in recent years. This allows MILS-based systems to host applications and data of multiple security classifications concurrently on a uniprocessor platform at affordable cost. In this paper, the potential requirements for the implementation of a separation kernel to support MILS systems on multicore processor architectures will be considered, and the design challenges associated with its potential implementation on the NXP (formerly Freescale) QorIQ™ P4080 multicore processor will be discussed. Finally, the potential use of a MILS Multicore separation kernel in two use cases will be presented - a Cross-Domain System (CDS) network gateway, and a Multi-Level Secure (MLS) Integrated Modular Avionics (IMA) platform