We present results of the MUSE-ALMA haloes, an ongoing study of the circumgalactic medium (CGM) of low-redshift galaxies (z ≤ 1.4), currently comprising 14 strong H I absorbers in 5 quasar fields. We detect 43 galaxies associated with absorbers down to star formation rate (SFR) limits of 0.01-0.1 M_☉ yr^-1, found within impact parameters (b) of 250 kpc from the quasar sightline. Excluding the targeted absorbers, we report a high detection rate of 89 per cent and find that most absorption systems are associated with pairs or groups of galaxies (3-11 members). We note that galaxies with the smallest impact parameters are not necessarily the closest to the absorbing gas in velocity space. Using a multiwavelength data set (UVES/HIRES, HST, MUSE), we combine metal and H I column densities, allowing for derivation of the lower limits of neutral gas metallicity as well as emission-line diagnostics (SFR, metallicities) of the ionized gas in the galaxies. We find that groups of associated galaxies follow the canonical relations of N(H I)-b and W_r(2796)-b, defining a region in parameter space below which no absorbers are detected. The metallicity of the ISM of associated galaxies, when measured, is higher than the metallicity limits of the absorber. In summary, our findings suggest that the physical properties of the CGM of complex group environments would benefit from associating the kinematics of individual absorbing components with each galaxy member....