We consider discrete-event systems (DES) whose logical component is characterized by a constraint set and,whose temporal mechanism involves synchronization of the clock sequence with a master clock, We are interested in determining sufficient conditions on the constraint sets of a family of such synchronous DES that ensure that the event counting process of one system dominates the convex combination of the event counting processes of a collection of systems Our point of departure is a result due to Glasserman and Yao [16], which established a sufficient condition based on characteristic functions, First me show that the characteristic function condition is equivalent to a simpler condition on the score spaces themselves, As both of these (equivalent) conditions are rather strong, however, we introduce coevality to obtain weaker sufficient conditions, To demonstrate the scope of these two results, we prove the near-concavity of the throughput in various parameters for min-linearly constrained DES. This not only covers various known concavity results for tandems, cycles, and fork-join networks of stations with general blocking and starvation, but also establishes new ones for certain classes of networks which involve splitting and merging traffic streams, These results are finally extended to the class of generalized min-linearly constrained DES,