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In this paper we consider a multi-class, multi-server queueing system with non-preemptive priorities. We distinguish two groups of priority classes that consist of multiple items, each having their own arrival and service rate. We assume Poisson arrival processes and exponentially distributed service times. We derive an approximation method to estimate the steady state probabilities with an approximation error that can be made as small as desired at the expense of some more numerical matrix iterations. Based on these probabilities, we can derive approximations for a wide range of relevant performance characteristics, such as the expected postponement time for each item class and the first and second moment of the number of items of a certain type in the system.