Results. We report the discovery of three new dwarf galaxies in the vicinity of the brightest member of the Sculptor filament, the late-type spiral NGC 253, located at a distance of 3.7 Mpc towards Anti-Virgo. We name them Do II, Do III, and Do IV. Assuming they are companions of NGC 253, their total absolute V-magnitudes fall in the -7 to -9 mag range, which is typical for dwarf satellites in the local Universe. The central surface brightness tends to be extremely low for all three discovered dwarfs and falls roughly in the range of 25-26 mag arcsec(-2) in g-band. Using known data on distances and velocities of galaxies, we estimate the total virial mass of the NGC 253 group to be 8 x 10(11)M(circle dot), which gives a virial radius of R-200 = 186 kpc and a turn-around radius of 706 kpc. We also discuss the possible existence of a spatially flattened and velocity-correlated satellite system around NGC 253. This large-scale structure is orientated almost edge-on to the line of sight. The possible plane of satellites is only 31 kpc thick with a minor-to-major axis ratio of 0.14. Four out of five galaxies with measured velocities follow a common velocity trend similar to those observed in the planes of satellites around the Andromeda and Centaurus A galaxies. However, the small number of galaxies with known velocities prevents us from reaching a definitive conclusion about the formation scenario of the structure and its possible relation to the surrounding cosmic web.