Abstract Modular supervisory control is motivated by the gain in complexity of control synthesis of supervisors. Sufficient conditions for maximal permissiveness of supervisors include mutual controllability and mutual normality. In this paper, we show how these conditions can be weakened. Namely, we can relax the requirement that the conditions hold for all pairs of components by putting the tuples of plants that do not satisfy the given condition for maximal permissiveness into different groups on an intermediate level of abstraction.