We present a comprehensive and sensitive unbiased survey of interstellar features in the near-UV range (3050-3700{AA}). We combined a large number of VLT/UVES archival observations of a sample of highly reddened early-type stars -typical diffuse interstellar band targets- and unreddened standards. We stacked the individual observations to obtain a reddened "superspectrum" in the interstellar rest frame with a signal-to-noise ratio exceeding 1500. We compared this to the analogous geocentric and stellar rest frame superspectra as well as to an unreddened superspectrum to find interstellar absorption features. We find 30 known features (11 atomic and 19 molecular) and tentatively detect up to 7 new interstellar absorption lines of unknown origin. Our survey is sensitive to narrow and weak features; telluric residuals preclude us from detecting broader features. For each sightline, we measured fundamental parameters (radial velocities, line widths, and equivalent widths) of the detected interstellar features. We also revisit upper limits for the column densities of small, neutral polycyclic aromatic hydrocarbon molecules that have strong transitions in this wavelength range.