It remains difficult to interpret the near-IR emission of young stellar populations. One main reason is our incomplete understanding of the spectra of luminous red stars. This work provides a grid of theoretical spectra of red giant (RG) and red supergiant (RSG) stars, that extends through optical and near-IR wavelengths. For the first time, models are also provided with modified surface abundances of C, N and O, as a step towards accounting for the changes that occur due to convective dredge-up in red supergiants or may occur at earlier evolutionary stages in the case of rotation. The aims are (i) to assess how well current models reproduce observed spectra, in particular in the near-IR; (ii) to quantify the effects of the abundance changes on the spectra; and (iii) to determine how these changes affect estimates of fundamental stellar parameters.