We present the first results from our survey of intervening and proximate Lyman limit systems (LLSs) at $z$$sim$2.0-2.5 using the Wide Field Camera 3 on-board the Hubble Space Telescope. The quasars in our sample are projected pairs with proper transverse separations $R_perp$$leq$150 kpc and line of sight velocity separations $lesssim$11,000 km/s. We construct a stacked ultraviolet (rest-frame wavelengths 700-2000AA) spectrum of pairs corrected for the intervening Lyman forest and Lyman continuum absorption. The observed spectral composite presents a moderate flux excess for the most prominent broad emission lines, a $sim$30% decrease in flux at $lambda$=800-900AA compared to a stack of brighter quasars not in pairs at similar redshifts, and lower values of the mean free path of the HI ionizing radiation for pairs ($lambda_{rm mfp}^{912}=140.7pm20.2~h_{70}^{-1}$Mpc) compared to single quasars ($lambda_{rm mfp}^{912}=213.8pm28~h_{70}^{-1}$Mpc) at the average redshift $zsimeq2.44$. From the modelling of LLS absorption in these pairs, we find a higher ($sim$20%) incidence of proximate LLSs with $log N_{rm HI}geq17.2$ at $delta v$$<$5,000 km/s compared to single quasars ($sim$6%). These two rates are different at the 5$sigma$ level. Moreover, we find that optically-thick absorbers are equally shared between foreground and background quasars. Based on these pieces of evidence, we conclude that there is a moderate excess of gas absorbing Lyman continuum photons in our closely-projected quasar pairs compared to single quasars. We argue that this gas arises mostly within large-scale structures or partially neutral regions inside the dark matter haloes where these close pairs reside.
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