A typical group mutual exclusion algorithm among m groups makes use of anm-group coterie, which determines the performance of the algorithm. There are two main performance measures: The availability is the probability that an algorithm tolerates process crash failures, and the concurrency is the number of processes that it allows simultaneous access to the resources. Since non-dominated (ND, for short) m-group coteries (locally) maximize the availability and their degrees roughly correspond to the concurrency, methods to construct ND m-group coteries with large degrees are looked for. Nevertheless, only a few naive methods have been proposed. This paper presents three methods to construct desirable m-group coteries. The first method constructs an ND m-group coterie from a dominated one using the transversal composition. The second one constructs an ND (m - 1)-group coterie from an ND m-group coterie. The last one uses the coterie join operation to produce an ND m-group coterie from an ND coterie and another ND mgroup coterie. These methods preserve the degrees of the original m-group coteries.