  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.
