  We examine to what extent disk and outflow models can reproduce observations
of H I gas within a few virial radii of galaxies in pairs and groups. Using
highly-sensitive HST/COS and FOS spectra of the Q0107 quasar triplet covering
Ly$\alpha$ for z$\lesssim$1, as well as a deep galaxy redshift survey including
VIMOS, DEIMOS, GMOS and MUSE data, we test simple disk and outflow models
against the H I absorption along three lines-of-sight (separated by 200-500
kpc) through nine galaxy groups in this field. These can be compared with our
previous results in which these models can often be fit to the absorption
around isolated galaxies. Our models can reproduce $\approx$ 75$\%$ of the 28
identified absorption components within 500 km/s of a group galaxy, so most of
the H I around groups is consistent with a superposition of the CGM of the
individual galaxies. Gas stripped in interactions between galaxies may be a
plausible explanation for some of the remaining absorption, but neither the
galaxy images nor the galaxy and absorber kinematics provide clear evidence of
such stripped material, and these unexplained absorbers do not preferentially
occur around close pairs of galaxies. We find H I column densities typically
higher than at similar impact parameters around isolated galaxies ($\approx$
2.5$\sigma$), as well as more frequent detections of O VI than around isolated
galaxies (30$\%$ of sightlines to 7$\%$).
