Galaxy mergers and gas accretion from the cosmic web drove the growth of galaxies and their central black holes at early epochs. We report spectroscopic imaging of a multiple merger event in the most luminous known galaxy, WISE J224607.56-052634.9 (W2246-0526), a dust-obscured quasar at redshift 4.6, 1.3 billion years after the Big Bang. Far-infrared dust continuum observations show three galaxy companions around W2246-0526 with disturbed morphologies, connected by streams of dust likely produced by the dynamical interaction. The detection of tidal dusty bridges shows that W2246-0526 is accreting its neighbors, suggesting that merger activity may be a dominant mechanism through which the most luminous galaxies simultaneously obscure and feed their central supermassive black holes.