With close pairs of quasars at different redshifts, a background quasar sight line can be used to study a foreground quasar's environment in absorption. We search 149 moderate-resolution background quasar spectra from Gemini, Keck, the MMT, and the SDSS to survey Lyman limit systems (LLSs) and damped Ly{alpha} systems (DLAs) in the vicinity of 1.8<z<4.0 luminous foreground quasars. A sample of 27 new quasar-absorber pairs is uncovered with column densities 10^17.2^cm^-2^<NH<10^20.9^cm^-2^ and transverse (proper) distances of 22h^-1^kpc<R<1.7h^-1^Mpc from the foreground quasars.