Coalitional Normative System (CNS) is an extension of a Normative System (NS) by enabling selective constraining a coalition’s joint behavior. The study extends the semantics of ATL and proposes Coordinated ATL (Co-ATL) to support the formalizing of CNS. The paper classifies all the CNSs that control the same coalition into the same class and characterizes the power limitation of each such class by identifying two fragments of Co-ATL language corresponding to two types of system properties that are unchangeable. The relation between NS and CNS is discussed, and it turns out that by the result better characterize the power limitation of NS. Moreover, the study extends further the CNS by including a finite state machine encoding the execution history, and results show that the power limitation characterization for CNS is invariant under this extension.