||We present a modeling framework for the mutation of social groups under internal and external pressure. This framework enables the simultaneous study of group mutability- relevant phenomena studied across psychology, sociology, and economics, and manifesting at the level of the social group, a pairwise interaction, and even individual perception. We investigate cases where individuals leave, or remain in, a group external to the coalition. We quantify a group-member's relative attachment to the group, which can be used to predict the least satisfied members of a group and thus the most likely to leave. This is especially important to characterize for internally- stable extremist groups, where individuals can be tactically targeted with incentives (e.g., money, information campaigns) to create division within the group structure, and where such knowledge can remove the need for costly and dangerous tactical interventions. We explicitly compute the relative stability of a group under one such model, and describe social norms that would lead to the most stable external group. We have shown, paradoxically, that a stable inequity-unconstrained norm will lead to redistribution effects compensating individuals for the negative externalities of group membership, while an inequity- constrained stable norm results in a more unequal, and thus more unstable, external group.