Element abundances in distant galaxies are an important probe of the star formation and feedback processes in galaxies. Damped and sub-damped Lyman-alpha absorbers detected in quasar spectra offer important probes of the chemistry of distant gas-rich galaxies. Especially important for determining dust-free metallicity measurements are the abundances of volatile elements such as S, O, Zn that do not deplete much on interstellar dust grains. Previous work led by the authors has shown that sub-DLAs at redshifts less than 2 are more metal-rich than DLAs on average. On the other hand, the difference between DLAs and sub-DLAs may not be as significant at z ~5. However, the current knowledge of how the abundances of volatile elements in sub-DLAs and DLAs compare at intermediate redshifts is relatively sparse. As a step toward bridging this gap,here we present abundance measurements of Zn, S, O (as well as those of C, Si and Fe) for four sub-DLAs at redshifts between 2 and 3 using observations obtained with the MIKE spectrograph on the Magellan telescope. Using the volatile elements, we find 3 of the 4 absorbers to be fairly metal-rich: between 20% solar to 2.5 times solar, i.e. more metal-rich compared to DLAs at these redshifts. We put constraints on the electron densities using the fine structure lines of C II⋆ andSi II⋆ for two of the sub-DLAs, and find these values to be much higher than the median values found in DLAs in the literature. Furthermore, we estimate the cooling rate for an absorber at z=2.2, that suggests a higher star formation rate (SFR) density than the typical SFR density for DLAs at similar redshifts. We also study the metallicity versus velocity dispersion relation for our absorbers and compare with measurements from the literature. Most of our absorbers follow the expected trend from the corresponding relation for lower-redshift sub-DLAs. Finally, we search for CO AX absorption bands in these absorbers, but report non-detections. We acknowledge support from NASA grant NNX17AJ26G and NSF grants AST-0908890 and2009811.