SHADOWS [1, 2] is an intended future beam dump experiment in the CERN North Area, aiming to search for feebly interacting particles (FIPs) [3] created in 400 GeV/c proton interactions. Due to its proposed off-axis location alongside the K12 beamline [4], the SHADOWS detector can be placed potentially very close to the beam dump, enabling it to search for FIPs in unexplored parts of the parameter space. In order to guarantee good quality of a potential signal, it is crucial to reduce any backgrounds of Standard Model particles as much as possible. The dominant background downstream the beam dump is caused by muons [1]. This introduces the need of a dedicated muon sweeping system consisting of magnetised iron blocks (MIBs) to actively mitigate this background component. We present the conceptional design studies in the framework of the Conventional Beams Working Group of the Physics Beyond Colliders Initiative at CERN [5, 6].