  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.
