In this article we address the problem of estimating minimum effective doses in dose-finding clinical trials of multidimensional treatment. We are motivated by a behavioral intervention trial where we introduce sedentary breaks to subjects with a goal to reduce their glucose level monitored over 8 hours. Each sedentary break regimen is defined by two elements: break frequency and break duration. The trial aims to identify minimum combinations of frequency and duration that shift mean glucose, that is, the minimum effective dose (MED) combinations. The means of glucose reduction associated with the dose combinations are only partially ordered. To circumvent constrained estimation due to partial ordering, we propose estimating the MED by maximizing a weighted product of combinationwise posterior gains. The estimation adopts an asymmetric gain function, indexed by a decision parameter ϵ, which defines the relative gains of a true negative decision and a true positive decision. We also introduce an adaptive ϵ-tapering algorithm to be used in conjunction with the estimation method. Simulation studies show that using asymmetric gain with a carefully chosen ϵ is critical to keeping false discoveries low, while ϵ-tapering adds to the probability of identifying truly effective doses (i.e., true positives). Under an ensemble of scenarios for the sedentary break study, ϵ-tapering yields consistently high true positive rates across scenarios and achieves about 90% true positive rate, compared to 68% by a nonadaptive design with comparable false discovery rate.