We calculate the mean-field phase diagram of a zero-temperature, binary Bose mixture on a square optical lattice, where one species possesses a non-negligible dipole moment. Remarkably, this system exhibits supersolidity for anomalously weak dipolar interaction strengths, which are readily accessible with current experimental capabilities. The supersolid phases are robust, in that they occupy large regions in the parameter space. Further, we identify a first-order quantum phase transition between supersolid and superfluid phases. Our results demonstrate the rich features of the dipolar Bose mixture, and suggest that this system is well-suited for exploring supersolidity in the experimental setting.
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