We present high-resolution spectroscopic measurements of the abundances of the {alpha} element titanium (Ti) and s-process elements yttrium (Y) and lanthanum (La) for 59 candidate M giant members of the Sagittarius (Sgr) dwarf spheroidal (dSph) + tidal tail system pre-selected on the basis of position and radial velocity (RV). As expected, the majority of these stars show peculiar abundance patterns compared to those of nominal Milky Way (MW) stars, but as a group, the stars form a coherent picture of chemical enrichment of the Sgr dSph from [Fe/H]=-1.4 to solar abundance. Finally, we analyze the chemical abundances of a moving group of M giants among the Sgr leading arm stars at the North Galactic Cap, but having RVs unlike the infalling Sgr leading arm debris there. Through use of "chemical fingerprinting," we conclude that these mostly receding northern hemisphere M giants also are Sgr stars, likely trailing arm debris overlapping the Sgr leading arm in the north.