We present moderate resolution spectroscopy of 111 cool dwarf stars to supplement the observations we have already presented in the Palomar/MSU Nearby-Star Spectroscopic Survey. The sample consists of 71 suspected nearby stars added to the Preliminary Third Catalog of Nearby Stars since 1991 as well as 40 faint red stars selected from the LHS catalog. The study was aimed at identifying interesting red dwarfs, particularly new nearby, ultracool dwarfs, and very metal-poor stars. The observations were made using the Palomar 60-inch, the Hale 200-inch and the Las Campanas 100-inch telescopes between June 1995 and January 1996. The spectral resolution is approximately 3 Angstroms per pixel with wavelength coverage from 6200 to 7500 Angstroms. Table 2 contains bandstrengths for TiO, CaH, and CaOH indices.