We present a study of rare decay modes B+→Ds+h0, B+→Ds∗+h0, and B+→D+h0, where h0 denotes the neutral meson η or K0, using a data sample of (772±10)×106 BB¯ events produced at the ϒ(4S) resonance. The data were collected by the Belle detector operating at the asymmetric-energy KEKB collider. We find no evidence for these decays, so we set upper limits at the 90% confidence level on the branching fractions of B+→Ds+h0, Ds∗+h0, and D+h0 decay modes. Along with these rare decay modes, we report improved measurements of the color-suppressed decay branching fractions B(B¯0→D0η)=(26.6±1.2±2.1)×10-5 and B(B¯0→D0K̄0)=(5.6±0.5±0.2)×10-5. The first and second quoted uncertainties are statistical and systematic, respectively. © 2023 authors. Published by the American Physical Society.