We study a model of four reduced staggered fields transforming in the bifundamental representation of a $SU(2)\times SU(2)$ symmetry group where just one of the SU(2) factors is gauged. This field content and symmetries are similar to a Higgs-Yukawa model that has been studied recently. The key observation in the latter work is that fermions acquire masses at strong coupling via the formation of a symmetric four fermion condensate in contrast to the more usual symmetry breaking bilinear condensate seen in eg. NJL models. The current work attempts to see whether this structure survives when the four fermi interactions are replaced by gauge interactions and to explore the resulting phase diagram.