Using a two-orbital model and Monte Carlo simulations, we investigate the effect of nonmagnetic B-site substitution on half-doped CE-type manganites. The lattice defects induced by this substitution destabilize the CE phase, which transforms into (1) the ferromagnetic (FM) metallic competing state, or (2) a regime with short-range FM clusters, or (3) a spin-glass state, depending on couplings and on the valence of the B-site substitution. While a C-type antiferromagnetic state is usually associated with an average $e_{rm g}$ charge density less than 0.5, the nonmagnetic B-site substitution that lowers the $e_{rm g}$ charge density is still found to enhance the FM tendency in our simulations. The present calculations are in qualitative agreement with experiments and provide a rationalization for the complex role of nonmagnetic B-site substitution in modulating the phase transitions in manganites.
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