  We discuss the representations that new scalar degrees of freedom (beyond
those in the minimal standard model) can have if they couple to quarks in a way
that is consistent with minimal flavor violation. If the new scalars are
singlets under the flavor group then they must be color singlets or color
octets. In this paper we discuss the allowed representations and renormalizable
couplings when the new scalars also transform under the flavor group. We find
that color \bar{3} and 6 representations are also allowed. We focus on the
cases where the new scalars can have renormalizable Yukawa couplings to the
quarks without factors of the quark Yukawa matrices. The renormalizable
couplings in the models we introduce automatically conserve baryon number.
