This is the third installment of the Galactic O-Star Spectroscopic Survey (GOSSS), a massive spectroscopic survey of Galactic O stars, based on new homogeneous, high signal-to-noise ratio, R ˜ 2500 digital observations selected from the Galactic O-Star Catalog. In this paper, we present 142 additional stellar systems with O stars from both hemispheres, bringing the total of O-type systems published within the project to 590. Among the new objects, there are 20 new O stars. We also identify 11 new double-lined spectroscopic binaries, 6 of which are of O+O type and 5 of O+B type, and an additional new tripled-lined spectroscopic binary of O+O+B type. We also revise some of the previous GOSSS classifications, present some egregious examples of stars erroneously classified as O-type in the past, introduce the use of luminosity class IV at spectral types O4-O5.5, and adapt the classification scheme to the work of Arias et al. The GOSSS spectroscopic data in this article were gathered with five facilities: the 1.5 m Telescope at the Observatorio de Sierra Nevada (OSN), the 2.5 m du Pont Telescope at Las Campanas Observatory (LCO), the 3.5 m Telescope at Calar Alto Observatory (CAHA), and the 4.2 m William Herschel Telescope (WHT) and 10.4 m Gran Telescopio Canarias (GTC) at Observatorio del Roque de los Muchachos (ORM).