Agents' valuations are interdependent if they depend on the signals of all agents. Previous literature has claimed that with interdependent valuations and multidimen-sional, but independent, signals, efficient auction design is impossible. This paper shows that, on the contrary, it is always possible to find efficient auction mechanisms. Furthermore, it characterizes the conditions under which it is possible to extract the full surplus from the agents. Finally, it shows that it is also possible to provide agents with the incentives for the efficient, ex-ante acquisition of information. All these results rest on the application of a generalized version of the revelation principle, which requires that the designer uses two reporting stages.