Symbiotic stars (SySt) are binaries composed of a star in the later stages of evolution and a stellar remnant. The enhanced mass-loss from the giant drives interacting mass exchange and makes these systems laboratories for understanding binary evolution. Studies of the chemical compositions are particularly useful since this parameter has strong impact on the evolutionary path. The previous paper in this series presented photospheric abundances for 24 giants in S-type SySt enabling a first statistical analysis. Here we present results for an additional sample of 13 giants. The aims are to improve statistics of chemical composition involved in the evolution of SySt, to study evolutionary status, mass transfer and to interpret this in terms of Galactic populations. High-resolution, near-IR spectra are used, employing the spectrum synthesis method in a classical approach, to obtain abundances of CNO and elements around the iron peak (Fe, Ti, Ni). Low-resolution spectra in the region around the Ca II triplet were used for spectral classification. The metallicities obtained cover a wide range with a maximum around ~-0.2 dex. The enrichment in the 14N isotope indicates that these giants have experienced the first dredge-up. Relative O and Fe abundances indicate that most SySt belong to the Galactic disc; however, in a few cases, the extended thick-disc/halo is suggested. Difficult to explain, relatively high Ti abundances can indicate that adopted microturbulent velocities were too small by ~0.2-0.3 km/s. The revised spectral types for V2905 Sgr, and WRAY 17-89 are M3 and M6.5, respectively.
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