Past laboratory experiments at high energy density have provided insights into the physics of supernovae, supernova remnants, and the destruction of interstellar clouds. In a typical experimental setting, a laser-driven planar blast wave interacts with a compositionally homogeneous spherical or cylindrical target. In this work we propose a new laboratory platform that accounts for curvature of the impacting shock and density stratification of the target. Both characteristics reflect the conditions expected to exist shortly after a supernova explosion in a close binary system. We provide details of a proposed experimental design (laser drive, target configuration, diagnostic system), optimized to capture the key properties of recent ejecta–companion interaction models. Good qualitative agreement found between our experimental models and their astrophysical counterparts highlights the strong potential of the proposed design to probe details of the ejecta–companion interaction for broad classes of objects by means of laboratory experiments at high energy density.