  We present detailed chemical compositions of four stars on the first-ascent
red giant branch that are classified as chemically peculiar, but lack
comprehensive analyses at high spectral resolution. For BD+03{\deg}2688, HE
0457-1805, HE 1255-2324, and HE 2207-1746, we derived metallicities [Fe/H]
$=-1.21$, $-0.19$, $-0.31$, and $-0.55$, respectively, indicating a range in
Galactic population membership. In addition to atmospheric parameters, we
extracted elemental abundances for 28 elements, including the
evolutionary-sensitive CNO group and $^{12}$C/$^{13}$C ratios. Novel results
are also presented for the heavy elements tungsten and thallium. All four stars
have very large enhancements of neutron-capture elements, with high [La/Eu]
ratios indicating enrichments from the slow neutron capture ($s$-process). To
interpret these abundances, all indicative of [$s$/Fe] $> 1.0$, we compared our
results with data from literature, as well as with predictions from the Monash
and FRUITY $s$-process nucleosynthesis models. BD+03{\deg}2688, HE 1255-2324,
and HE 2207-1746 show C/O $>1$, while HE 0457-1805 has C/O $<1$. Since HE
0457-1805 and HE 1255-2324 are binary stars, their peculiarities are
attributable to mass transfer. We identified HE 0457-1805 as a new barium giant
star, and HE 1255-2324 as a new CH star, in fact a higher metallicity analogue
CEMP-$r/s$ star; the single object reported in literature so far with similar
characteristics is the barium star HD 100503 ([Fe/H] $= -0.72$). A systematic
monitoring is needed to confirm the binary nature of BD+03{\deg}2688 and HE
2207-1746, which are probably CH stars.
