We study the distribution and dynamics of the circumgalactic and intergalactic medium using a dense galaxy survey covering the field around the Q0107 system, a unique z ≈ 1 projected quasar triplet. With full Ly α coverage along all three lines-of-sight from z = 0.18 to z = 0.73, more than 1200 galaxy spectra, and two MUSE fields, we examine the structure of the gas around galaxies on 100-1000 kpc scales. We search for H i absorption systems occurring at the same redshift (within 500 km s-1) in multiple sightlines, finding with >99.9 per cent significance that these systems are more frequent in the observed quasar spectra than in a randomly distributed population of absorbers. This is driven primarily by absorption with column densities N(H i) > 1014 cm-2, whilst multi-sightline absorbers with lower column densities are consistent with a random distribution. Star-forming galaxies are more likely to be associated with multi-sightline absorption than quiescent galaxies. HST imaging provides inclinations and position angles for a subset of these galaxies. We observe a bimodality in the position angle of detected galaxy-absorber pairs, again driven mostly by high-column-density absorbers, with absorption preferentially along the major and minor axes of galaxies out to impact parameters of several hundred kpc. We find some evidence supporting a disc/outflow dichotomy, as H i absorbers near the projected major axis of a galaxy show line-of-sight velocities that tend to align with the rotation of that galaxy, whilst minor-axis absorbers are twice as likely to exhibit O vi at the same redshift.