We study the incidence of group and filamentary dwarf galaxy accretion into MilkyWay (MW) mass haloes using two types of hydrodynamical simulations: EAGLE, which resolves a large cosmological volume, and the AURIGA suite, which are very high resolution zoom-in simulations of individual MW-sized haloes. The present-day 11 most massive satellites are predominantly (75 per cent) accreted in single events, 14 per cent in pairs, and 6 per cent in triplets, with higher group multiplicities being unlikely. Group accretion becomes more common for fainter satellites, with 60 per cent of the top 50 satellites accreted singly, 12 per cent in pairs, and 28 per cent in richer groups. A group similar in stellar mass to the Large Magellanic Cloud would bring on average 15 members with stellar mass larger than 10(4) M-circle dot. Half of the top 11 satellites are accreted along the two richest filaments. The accretion of dwarf galaxies is highly anisotropic, taking place preferentially perpendicular to the halo minor axis, and, within this plane, preferentially along the halo major axis. The satellite entry points tend to be aligned with the present-day central galaxy disc and satellite plane, but to a lesser extent than with the halo shape. Dwarfs accreted in groups or along the richest filament have entry points that show an even larger degree of alignment with the host halo than the full satellite population. We also find that having most satellites accreted as a single group or along a single filament is unlikely to explain the MW disc of satellites.