We describe a superconducting Casimir apparatus inspired by a recently proposed setup involving magnetic surfaces [G. Bimonte, Phys. Rev. Lett. {\bf 112}, 240401 (2014)]. The present setup consists of a superconducting Nb sphere and a flat gold plate including in its interior a superconducting Nb strip. The experimental scheme involves a differential measurement of the Casimir force at a point of the gold plate above the Nb strip and away from from it. We show that similar to the previous setup, the superconducting system considered here implies widely different modulations of the Casimir force, depending on whether the thermal force is computed using the Drude or the plasma model, thus paving the way to an unambiguous discrimination between these alternative prescriptions.