We present initial results of a survey of host L-* galaxies environments in the Local Volume (D < 10 Mpc) searching for satellite dwarf galaxy candidates using the wide-field Hyper Suprime-Cam imager on the 8 m Subaru Telescope. This paper presents complete results on NGC2683 (M-BT,M-0 = -19.62, D = 9.36 Mpc, v circle dot = 411 km s(-1)), an isolated Sc spiral galaxy in the Leo Spur. At the distance of NGC2683, we image the complete volume out to projected radii of 380 kpc using a hexagonal arrangement of 7 pointings. Direct inspection of the images is complete down to M-g similar to -11 and has revealed four new satellite galaxy candidates, two of which have been independently discovered by other researchers. Assuming the distance of NGC2683, these candidates span luminosities -12 < M-g < -9 and effective radii 150 pc < r(e) < 1100 pc and are found to be morphologically reminiscent of satellite galaxies in the Local Group. These four new candidates add to the eight already known. A principle component analysis of the 2D projected distribution of the 12 satellite galaxies of NGC2683 reveals a flattened projected disc of satellites, with axis ratio b/a = 0.23. This flattening in the 2D projected system of satellites is a 1 per cent outlier of simulated isotropic satellite systems but is mostly consistent with satellite distributions of comparable galaxy environments in the IllustrisTNG simulation. This indicates the possible presence of a satellite plane, which will need to be investigated with follow-up observations.