Over the last decade, large-scale multiple testing has found itself at the forefront of modern data analysis. In many applications data are correlated, so that the observed test statistic used for detecting a non-null case, or signal, at each location in a dataset carries some information about the chances of a true signal at other locations. Brown, Lazar, Datta, Jang, and McDowell (2014) proposed in the neuroimaging context a Bayesian multiple testing model that accounts for the dependence of each volume element (voxel) on the behavior of its neighbors through a conditional autoregressive (CAR) model. Here, we propose more general definitions of neighborhood structures that allow for inclusion of points with no neighbors at all, something that is not possible under conventional CAR models. We also consider neighborhoods based on criteria other than physical location, such as genetic pathways in microarray defined based on existing biological knowledge. This modification allows for the simultaneous modeling of dependent and independent cases, resulting in increased precision in the estimates of non-null signal strengths. Further, we allow for less restrictive prior assumptions on the variance components, justify the selected prior distribution, and prove that the resulting posterior distribution is proper. We illustrate the effectiveness and applicability of our proposed model by using it to analyze both simulated and real microarray data in which the genes exhibit nontrivial dependence that is determined by physical adjacency on a chromosome or predefined gene pathways.