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Systems in many safety-critical application domains are subject to certification requirements. In such a system, there are typically different applications providing functionalities that have varying degrees of criticality. Consequently, the certification requirements for functionalities at these different criticality levels are also varying, with very high levels of assurance required for a highly critical functionality, whereas relatively low levels of assurance required for a less critical functionality. Considering the timing assurance given to various applications in the form of guaranteed budgets within deadlines, a theory of real-time scheduling for such multi-criticality systems has been under development in the recent past. In particular, an algorithm called Earliest Deadline First with Virtual Deadlines (EDF-VD) has shown a lot of promise for systems with two criticality levels, especially in terms of practical performance demonstrated through experiment results. In this paper we design a new schedulability test for EDF-VD that extend these performance benefits to multi-criticality systems. We propose a new test based on demand bound functions and also present a novel virtual deadline assignment strategy. Through extensive experiments we show that the proposed technique significantly outperforms existing strategies for a variety of generic real-time systems.