Few gene-environment interactions (G × E) have been discovered in cancer epidemiology thus far, in part due to the large number of possible G × E to be investigated and inherent low statistical power of traditional analytic methods for discovering G × E. We consider simultaneously testing for interactions between several related exposures and a genetic variant in a genome-wide study. To improve power, constrained testing strategies are proposed for multivariate gene-environment interactions at two levels: interactions that have the same direction (one-sided or bidirectional hypotheses) or are proportional to respective exposure main effects (a variant of Tukey's one-degree test). Score statistics were developed to expedite the genome-wide computation. We conducted extensive simulations to evaluate validity and power performance of the proposed statistics, applied them to the genetic and environmental exposure data for esophageal adenocarcinoma and Barrett's esophagus from the Barretts Esophagus and Esophageal Adenocarcinoma Consortium (BEACON), and discovered three loci simultaneously interacting with gastresophageal reflux, obesity, and tobacco smoking with genome-wide significance. These findings deepen understanding of the genetic and environmental architecture of Barrett's esophagus and esophageal adenocarcinoma.