This article develops a new approach to a family of hierarchy-effect inducing configurations, with a focus on Person Case Constraint effects, dative-nominative configurations, and copula constructions. The main line of approach in the recent literature is to attribute these effects to failures of φ-Agree or, more specifically, failures of nominal licensing or case checking. We propose that the problem in these configurations is unrelated to nominal licensing, but is instead the result of a probe participating in more than one Agree dependency, a configuration we refer to as feature gluttony. Feature gluttony does not in and of itself lead to ungrammaticality; rather, it can create irresolvably conflicting requirements for subsequent operations. We argue that in the case of clitic configurations, a probe that agrees with more than one DP creates an intervention problem for clitic doubling. In violations involving morphological agreement, gluttony in features may result in a configuration with no available morphological output.