Our recent statistical investigations of broad UV lines of luminous QSOs suggest that the traditional broadline region (BLR) consists of two components-one of width -2000 km s-1 FWHM with the peak within a few hundred kilometers per second of the systemic redshift, and another very broad component of width greater-than-or-equal-to 7000 km s-1 FWHM and blueshifted by greater-than-or-equal-to 1000 km s-1. Differences in the relative strengths of these components account for much of the diversity of broad-line profiles, as well as relations among line strength, fine width, asymmetry, and peak blueshift. We have suggested that the narrower component arises in a distinct intermediate-line region (ILR) that is an inner extension of the narrow-fine region (NLR). We form spectra of the ILR and very broad line region (VBLR) in two complementary ways. First, using a small sample of high-quality spectra, we difference two composite spectra, one with FWHM(CIV) approximately 3000 km s-1, the other FWHM(CIV) approximately 7000 km s-1 (essentially a VBLR spectrum)-revealing a narrower line spectrum with FWHM approximately 2000 km s-1. Second, we use a principal component analysis of 200 low signal-to-noise ratio spectra from the Large Bright Quasar Survey. The ILR is identified with the first principal component-that component accounting for most of the spectrum-to-spectrum variation. The VBLR spectrum is derived by subtracting this ILR from the mean spectrum. The two methods yield similar results, and the spectra of the ILR and VBLR are very different. Additional support for the existence of two components is the lack of a correlation between the equivalent widths of the ILR and VBLR. We discuss the relationships between the VBLR, the ILR, and the traditional NLR. The ILR line intensity ratios are distinctly different from those of the VBLR, with (relative to C IV lambda1549) stronger Lyalpha and weaker N V lambda1240, lambda1400 feature, He II lambda1640, O III] lambda1663, and Al III lambda1860. Comparison with other AGN emission-line regions shows that the ILR spectrum tends to be intermediate between that of the VBLR and that of gas more distant from the ionizing continuum, such as the NLR and extended Lyalpha nebulosity. Comparison of the spectra with results from photoionization models suggests that, compared with the VBLR, the ILR is about 10 times more distant from the ionizing continuum (approximately 1 pc), 100-1000 times less dense (10(10) cm-3), and has a smaller covering factor (less than or similar to 3%, compared with approximately 24% for the VBLR).