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The overall correctness of large-scale systems composed of many groups of replicas executing BFT protocols scales poorly with the number of groups. This is because the probability of at least one group being compromised (more than 1/3 faulty replicas) increases rapidly as the number of groups increases. In this paper we address this problem with a simple modification to Castro and Liskov's BFT replication that allows for arbitrary choice of n (number of replicas) and f (failure threshold). The price to pay is a more restrictive liveness requirement, and we present the design of a large-scale BFT replicated system that obviates this problem.