We consider extra dimensional descriptions of models where there are two
separate strongly interacting sectors contributing to electroweak symmetry
breaking (``topcolor'' type models). In the extra dimensional picture there
would be two separate (anti-de Sitter) bulks meeting on the Planck brane, with
each bulk having its own corresponding IR (TeV) brane. Sources for electroweak
symmetry breaking can then be localized on both of these IR branes, while the
different generations of fermions may be separated from each other. We describe
the modes propagating in such a setup, and consider the cases where the
electroweak symmetry breaking on either of the two IR branes come either from a
higgsless scenario (via boundary conditions) or a (top-)Higgs. We show that the
tension that exists between obtaining a large top quark mass and the correct
value of the Zb\bar{b} couplings in ordinary higgsless models can be largely
relieved in the higgsless--top-Higgs versions of the two IR brane models. This
may also be true in the purely higgsless--higgsless case, however since that
model is necessarily in the strongly coupled regime the tree-level results for
the properties of the third generation may get large corrections. A necessary
consequence of such models is the appearance of additional pseudo-Goldstone
bosons (``top-pions''), which would be strongly coupled to the third
generation.Comment: 34 pages, LaTeX, 6 figures. v2: figure 2 fixed, footnote, comments
and references adde