We present spectroscopic data for 16369 stellar targets within and/or toward 38 dwarf spheroidal galaxies and faint star clusters within the Milky Way halo environment. All spectra come from observations with the multiobject, fiber-fed echelle spectrographs M2FS at the Magellan/Clay telescope or Hectochelle at the MMT, reaching a typical limiting magnitude G<~21. Data products include processed spectra from all observations and catalogs listing estimates-derived from template model fitting-of line-of-sight velocity (median uncertainty 1.4km/s) effective temperature (255K), (base-10 logarithm of) surface gravity (0.59dex in cgs units), [Fe/H] (0.4dex) and [Mg/Fe] (0.27dex) abundance ratios. The sample contains multiepoch measurements for 3720 sources, with up to 15 epochs per source, enabling studies of intrinsic spectroscopic variability. The sample contains 6087 likely red giant stars (based on surface gravity), and 4492 likely members (based on line-of-sight velocity and Gaia-measured proper motion) of the target systems. The number of member stars per individual target system ranges from a few, for the faintest systems, to ~850 for the most luminous. For most systems, our new samples extend over wider fields than have previously been observed; of the likely members in our samples, 820 lie beyond 2 times the projected half-light radius of their host system, and 42 lie beyond 5 R_half_.