Isotopic analysis of heavy elements in individual stardust grains is important in testing and constraining theories of stellar nucleosynthesis. These analyses are challenging in that the grains are very small, the largest being perhaps a few microns in diameter, and contain only trace concentrations of heavy elements, generally on the order of ppm. In addition, isotopic analysis requires the suppression of isobaric interferences. We describe a unique instrument, based on resonant ionization mass spectrometry, that has successfully characterized such grains for the past several years, and report on some recent upgrades that significantly enhance the instrumental capabilities. The fundamental principles and operational details are discussed, along with illustrative results and plans for future modifications.