This paper introduces a generalization of the regression-discontinuity design (RDD). Traditionally, RDD is considered in a two-dimensional framework, with a single assignment variable and cutoff. Treatment effects are measured at a single location along the assignment variable. However, this represents a specialized (and straight-forward) application of the design; a more generalized and flexible conceptualization of RDD allows researchers to examine treatment effects along a multidimensional frontier using multiple assignment variables (such as math and reading scores) and cutoffs. In Section 1 of this paper, the authors present the generalized RDD by describing its required components, the treatment effects estimated, and advantages and limitations of the design. In Section 2, they describe two analytic approaches for estimating treatment effects for the generalized RDD. The first is the "multivariate approach," which estimates treatment effects along a multi-dimensional frontier via a regression model. This approach is based on the assumption that the researcher can model the selection mechanism completely if all assignment variables and their respective cutoffs are known and observed (as is the case for many accountability policy studies that use RDD). The second is an extension of an approach originally used by Gill et al. (2007), which we call the "centering" approach. They show that both the multivariate and centering approaches yield identical average treatment effect estimates, though they have distinct advantages and limitations. In Section 3, they present an application of the "multivariate" and "centering" approaches in an RDD example that evaluates the impacts of missing AYP under NCLB on student with disability (SWD) achievement scores. They also discuss scenarios when neither approach is appropriate for estimating treatment effects. (Contains 4 figures.)