The muX project at the Paul Scherrer Institut aims to perform high- resolution muonic atom X-ray spectroscopy for the extraction of nuclear charge radii of radioactive isotopes that can be handled only in microgram quantities. Measurements of the absolute charge radii of high-Z radioactive elements are complementary to the measurements of relative differences in mean-square radii along the isotopic chain available from laser spectroscopy. One of the major limitations of atomic structure calculations is related with the uncertainty of the nuclear charge radius. This is the case for the extraction of the Weinberg angle from atomic parity violation in ²²⁶Ra. A new approach to solve previous limitations of muonic atom X-ray spectroscopy experiments is the application of multiple muon transfer reactions in a high-pressure hydrogen gas cell with a small admixture of deuterium. The validity of this method has been demonstrated with a measurement with only 5 μg of gold.