Dense stellar environments as hosts of ongoing star formation increase the probability of gravitational encounters among stellar systems during the early stages of evolution. Stellar interaction may occur through non-recurring, hyperbolic, or parabolic passages (a so-called 'fly-by'), through secular binary evolution, or through binary capture. In all three scenarios, the strong gravitational perturbation is expected to manifest itself in the disc structures around the individual stars. Here, we present near-infrared polarized light observations that were taken with the SPHERE/IRDIS instrument of three known interacting twin-disc systems: AS 205, EM∗ SR 24, and FU Orionis. The scattered light exposes spirals likely caused by the gravitational interaction. On a larger scale, we observe connecting filaments between the stars. We analyse their very complex polarized intensity and put particular attention to the presence of multiple light sources in these systems. The local angle of linear polarization indicates the source whose light dominates the scattering process from the bridging region between the two stars. Further, we show that the polarized intensity from scattering with multiple relevant light sources results from an incoherent summation of the individuals' contribution. This can produce nulls of polarized intensity in an image, as potentially observed in AS 205. We discuss the geometry and content of the systems by comparing the polarized light observations with other data at similar resolution, namely with ALMA continuum and gas emission. Collective observational data can constrain the systems' geometry and stellar trajectories, with the important potential to differentiate between dynamical scenarios of stellar interaction