A search is performed for D (*) + mesons in the reactions pp → D ∗ + K S 0 X and pp → D *0 K + X using data collected at centre-of-mass energies of 7 and 8 TeV with the LHCb detector. For the D ∗ + K S 0 final state, the decays D *+ → D 0 π + with D 0 → K − π + and D 0 → K − π + π + π − are used. For D *0 K +, the decay D *0 → D 0 π 0 with D 0 → K − π + is used. A prominent D s1(2536)+ signal is observed in both D ∗ + K S 0 and D *0 K + final states. The resonances D 1 * (2700)+ and D 3 * (2860)+ are also observed, yielding information on their properties, including spin-parity assignments. The decay D 2 * (2573)+ → D ∗ + K S 0 is observed for the first time, at a significance of 6.9 σ, and its branching fraction relative to the D 2 * (2573)+ → D + K S 0 decay mode is measured.