This paper studies a cooperative model of multilateral deterrence with a focus on how parametric heterogeneities in the deterring group affect core formation. Alongside basic analysis, two notably contrasting results are derived. First, it is shown that no parametrically symmetric deterring group of size n>=4 can support a core allocation. Second, a sufficient condition for core existence is derived for "single-differing-agent" groups (groups in which all agents except one outlier are parametrically identical up to a positive scale factor) which does not depend upon the specific nature of the individual non-outliers, and thus holds for groups of arbitrarily large size. Finally, computational analysis of this condition is used to show that it holds in many cases in which the outlier is sufficiently dominant in either retaliatory capability or incentive to deter.