We are concerned with mixed-criticality systems where a set of low-criticality (LO) and high-criticality (HI) tasks share one processor and are scheduled under EDF-VD algorithm. EDF-VD implements two operation modes: LO and HI. In LO mode, one or more HI tasks may exceed their execution budgets, which then causes a change to HI mode in the system. In HI mode, HI tasks are assigned larger execution budgets at the cost of the LO tasks, which often need to be discarded. In some cases, however, we would like to allow some LO tasks to continue running on the processor in spite of switching to HI mode. To this end, we incorporate utilization caps into the original EDF-VD algorithm. The idea is to partition tasks on the processor, for example, according to functional dependencies, and assign them a portion the total utilization. EDF-VD then applies to each of these partitions individually and up to their corresponding utilization caps. If one HI task exceeds its execution budget in LO mode, this only affects the LO tasks in the same partition, but not LO tasks in other partitions which can continue running. We present a technique to optimally choose utilization caps for each partition and perform a large set of experiments based on synthetic data illustrating benefits of the proposed technique.