Complex decay pathways involving radiative and nonradiative relaxation after deep core-level ionization in argon are disentangled by a unique combination of several synchrotron radiation-based spectroscopic techniques. In particular, by comparing the results obtained from electron-ion coincidence, photon-ion coincidence, and x-ray emission measurements, we are able to distinguish the final ionic states produced in the cascade decay involving Kα and Kβ radiative decay and final ionic states produced by nonradiative cascade decay. High-resolution Auger electron spectroscopy is then used as a complementary tool to identify the LMM transitions contributing to the cascade decay. Ab initio calculations are performed to identify the electronic states involved in the LMM decay.