We present results from the remaining sources in our search for near-infrared (NIR) candidate counterparts to ultraluminous X-ray sources (ULXs) within ≃10 Mpc. We observed 23 ULXs in 15 galaxies and detected NIR candidate counterparts to 6 of them. Two of these have an absolute magnitude consistent with a single red supergiant (RSG). Three counterparts are too bright for an RSG and spatially extended, and thus we classify them as stellar clusters. The other candidate is too faint for an RSG. Additionally, we present the results of our NIR spectroscopic follow-up of five sources: four originally classified as RSG and one as a stellar cluster on the basis of previous photometry. The stellar cluster candidate is actually a nebula. Of the four RSG candidates, one source has a broad H α emission line redshifted by ∼z = 1, making it a background active galactic nucleus (AGN). Two other sources show stellar spectra consistent with them being RSGs. The final RSG candidate is too faint to classify, but does not show strong (nebular) emission lines in its spectrum. After our search for NIR counterparts to 113 ULXs, where we detected a candidate counterpart for 38 ULXs, we have spectroscopically confirmed the nature of 12: 5 sources are nebulae, 1 source is not classified, 1 source is an AGN, and 5 are RSGs. These possible five ULX-RSG binary systems would constitute ${\simeq} (4 \pm 2){{\ \rm per\ cent}}$ of the observed ULXs, a fraction almost four times larger than what was predicted by binary evolution simulations.