We consider a social choice setting with multidimensional signals and interdependent valuations. Such frameworks have been recently and increasingly used in order to study multi-object auctions. We obtain concise characterizations of ex-post implementable (not necessarily efficient) social choice functions in terms of affine functions that associate a weight to each agent and to each alternative. These characterizations can greatly reduce the complexity of the search for a constrained efficient (i.e., second best) mechanism in the generic cases where efficient outcomes cannot be implemented.