We describe a new approach to the magnetic measurement of liver iron stores, using an instrument that incorporates a combination of permanent magnets and superconducting flux transformers. Instead of traditional low-transition-temperature superconductor (LTS) transformers, the susceptometer employs their high-transition-temperature (HTS) counterparts. This innovation substantially reduces the size and weight of the instrument, allowing the whole assembly to be scanned in a horizontal plane. We report engineering details of the HTS flux transformers, magnet assembly, field sensing, and scan mechanism, and present experimental data to show that scanning susceptometer can determine not only the susceptibility of cylindrical phantom models but also their diameters. We conjecture that further refinements of scanning susceptometer could lead to a form of susceptibility imaging that would enhance the accuracy of measurements of liver iron stores and also lead to new medical applications of the method.