We analyzed high-order harmonic generation from the plasma plumes prepared on the surfaces of complex targets. The studies of $\mathrm{In}–\mathrm{Ag}$ targets showed that the characteristics of the high-order harmonics from the double-target plume were the same as those from the single-target plasmas. For the chromium–tellurium plasma, the enhancements of the 29th and 27th harmonics were obtained, thus indicating the appearance of the enhancement properties from both components of the double-target plasma. These comparative studies also showed higher enhancement of a single harmonic in the case of atomic plasma (Sb) with regard to the molecular one $\left(\mathrm{InSb}\right)$ . The additional component can only decrease the enhancement factor of the medium, due to the change of the oscillator strength and spectral distribution of the transitions involved in the resonance enhancement of the specific harmonic order. The theoretical calculations have shown the enhancement of specific harmonics for the Sb, Te, and Cr plasmas in the double-target configurations.