Using the analytic time-dependent effective range theory, we study two-color high-order harmonic generation (HHG) involving a weak extreme ultraviolet (XUV) pulse and an intense infrared laser field. Our analysis shows that XUV-assisted HHG spectra contain multiple additional plateau structures originating from absorption of one or more XUV photons at the photorecombination step of HHG. We show also that the HHG rate corresponding to the nth plateau can be presented in a factorized form involving the XUV-assisted (multiphoton) photorecombination cross section (PRCS) corresponding to absorption of n XUV photons of energy Ω and emission of a harmonic of energy Ω h. This factorization allows one to extract the PRCS from the HHG spectrum and to retrieve the cross section of the inverse process: the photoionization cross section involving absorption of a single photon of energy Ω h and emission of n XUV photons of frequency Ω. The analytic HHG results are in excellent agreement with numerical solutions of the 3D time-dependent Schrödinger equation. 44 in Refs. [32-35]. Studies of XUV-enhanced HHG on the 45 single-atom level have been carried out for either an at-46 tosecond pulse train [36-39] or an isolated attosecond 47 pulse [40, 41]. These studies have shown that the XUV 48 pulse or pulses can be employed to control the ionization 49 step and to select a specific electron trajectory contribut-50 ing to the HHG yield. The addition of a weak XUV field 51 was shown in Refs. [42, 43] to result in extensions of the 52 usual IR-field-induced HHG plateau. These plateau ex-53 tensions were found to be one-electron phenomena and 54 were attributed to XUV-field-induced ac-Stark modula-55 tions of the ground state and the returning EWP as re-56 combination occurs [43]. Studies have also been carried 57 out concerning the effects of XUV field population of res-58 onant excited states from the valence shell of an atom, 59 such as, e.g., Rabi oscillations [44-46]. 60 If the energy of the XUV photon is large enough, inner-61 shell electrons may become involved in the HHG process, 62 leading to an increase of the HHG plateau cutoff energy 63 owing to the larger binding energy of core electrons [47-64 49]. The addition of an XUV field also leads to an ex-65 tension of HHG spectroscopy methods that enable one to 66 obtain information about inner-electron dynamics. Such 67 extensions have been carried out to study Auger pro-68 cesses [50, 51] and effects of resonant XUV-induced core-69 valence shell transitions [52]. 70 Most studies cited above are focused on the HHG chan-71 nel involving absorption of an XUV photon during the 72 initial (ionization) step of the three-step HHG scenario. 73 However, even in the single-active-electron approxima-74 tion, there exist other channels for XUV-assisted HHG 75 that remain so far insufficiently explored. Some of these 76 additional channels may be ignored. Indeed, if the XUV 77 photon is emitted at the ionization step, it effectively in-78 creases the ionization energy of an intermediate (vir...