Mixed-criticality systems emerged with the aim of reconciling safety requirements and efficient use of multi-processor or uniprocessor platforms. On multi-processors, recent works on mixed-criticality have produced impressive results in terms of speed-up factor. But these solutions, based on Pfair-like scheduling algorithms, entail too many preemptions and migrations to be effectively used in real systems. As RUN is an optimal scheduling algorithm that is known to limit this problem, we propose MxC-RUN, an adaptation of RUN to mixed-criticality systems. We redefine RUN's primal servers as modal servers that allocate the overestimated time budget of their higher criticality tasks to execute lower criticality ones. These servers can be handled by RUN without any modification and preserve its performances in terms of preemptions and migrations. MxC-RUN earns a speed-up factor smaller than other multi-processors EDF-based mixed-criticality scheduling algorithms.