We present high S/N spectroscopy of 15 emission-line galaxies (ELGs) cataloged in the KPNO International Spectroscopic Survey (KISS), selected for their possession of high equivalent width [O III] lines. The primary goal of this study was to attempt to derive direct-method ($T_e$) abundances for use in constraining the upper-metallicity branch of the $R_{23}$ relation. The spectra cover the full optical region from [O II]{lambda}{lambda}3726,3729 to [S III]{lambda}{lambda}9069,9531 and include the measurement of [O III]{lambda}4363 in 13 objects. From these spectra, we determine abundance ratios of helium, nitrogen, oxygen, neon, sulfur, and argon. We find these galaxies to predominantly possess oxygen abundances in the range of 8.0 $lesssim$ 12+log(O/H) $lesssim$ 8.3. We present a comparison of direct-method abundances with empirical SEL techniques, revealing several discrepancies. We also present a comparison of direct-method oxygen abundance calculations using electron temperatures determined from emission lines of O$^{++}$ and S$^{++}$, finding a small systematic shift to lower $T_e$ (~1184 K) and higher metallicity (~0.14 dex) for sulfur-derived $T_e$ compared to oxygen-derived $T_e$. Finally, we explore in some detail the different spectral activity types of targets in our sample, including regular star-forming galaxies, those with suspected AGN contamination, and a local pair of low-metallicity, high-luminosity compact objects.