Dowker's Theorem provides a constructive, functorial homotopy equivalence between two canonical simplicial complexes constructed from a binary relation between a pair of sets. It arises in a variety of contexts in topology, and has recently been the subject of significant interest in applied contexts. We will review Dowker's Theorem and the Fiber Lemma that underlies both it and the (equivalent) Nerve Theorem. We will then describe a generalization of Dowker's Theorem to the context of three or more sets, where we construct a hierarchy of complexes analogous to the classical Dowker Complex. The "top level" complexes in this hierarchy are all homotopy equivalent, generalizing Dowker's Theorem, however we also find a variety of interesting and potentially distinct homotopy types that arise at "lower levels," suggesting a potentially rich interplay between the structure of these secondary complexes. This work originated in a workshop at the American Institute of Mathematics, and is a part of an ongoing collaboration with Vin de Silva, Vladimir Itskov, Michael Robinson, Radmila Sazdanovic, Niko Schonsheck, Melvin Vaupel, and Iris Yoon.