This paper proposes a Bayesian estimation framework for panel data sets with binary dependent variables where a large number of cross-sectional units are observed over a short period of time and cross-sectional units are interdependent in more than a single network domain. The latter provides for a substantial degree of flexibility towards modeling the decay function in network neighborliness (e.g., by disentangling the importance of rings of neighbors) or towards allowing for several channels of interdependence whose relative importance is unknown ex ante. Besides the flexible parameterization of cross-sectional dependence, the approach allows for simultaneity of the equations. These features should make the approach interesting for applications in a host of contexts involving structural and reduced-form models of multivariate choice problems at micro-, meso-, and macro-economic levels. The paper outlines the estimation approach, illustrates its suitability by simulation examples, and provides an application to study exporting and foreign ownership among potentially interdependent firms in the specialized and transport machinery sector in the province of Guangdong.