Mixed Criticality Systems (MCS) have gained increasing interest in the past few years due to their industrial relevance. When mixed-criticality systems are implemented on multicore architectures, several challenges arise such as the efficient partitioning of these systems. In this paper, we address this issue by presenting a novel mixed-criticality partitioning algorithm, the Dual-Partitioned Mixed-Criticality (DPM) algorithm, that allows limited migration of LO-criticality tasks to enhance the efficiency of the partitioning while maintaining many of the advantages of partitioned systems. Experimental results show that DPM consistently outperforms existing mixed-criticality partitioning algorithms, for example, at utilizations of 0.8 or higher, DPM is able to schedule 17% more systems.