We analyse 45 spectropolarimetric observations of the eclipsing, interacting binary star V356 Sgr, obtained over a period of ~21yr, to characterize the geometry of the system's circumstellar material. After removing interstellar polarization from these data, we find that the system exhibits a large intrinsic polarization signature arising from electron scattering. In addition, the lack of repeatable eclipses in the polarization phase curves indicates the presence of a substantial pool of scatterers not occulted by either star. We suggest that these scatterers form either a circumbinary disc coplanar with the gainer's accretion disc or an elongated structure perpendicular to the orbital plane of V356 Sgr, possibly formed by bipolar outflows. We also observe small-scale, cycle-to-cycle variations in the magnitude of intrinsic polarization at individual phases, which we interpret as evidence of variability in the amount of scattering material present within and around the system. This may indicate a mass-transfer or mass-loss rate that varies on the time-scale of the system's orbital period. Finally, we compare the basic polarimetric properties of V356 Sgr with those of the well-studied {beta} Lyr system; the significant differences observed between the two systems suggest diversity in the basic circumstellar geometry of Roche lobe overflow systems.