As part of the ongoing work of the R-Process Alliance (RPA), detailed abundance measurements of 29 heavy elements in three metal-poor stars, 2MASS J14592981−3852558, 2MASS J19445483−4039459, and 2MASS J15211026−0607566, are presented based on an analysis of high-resolution (R ∼ 80,000), high-signal-to-noise “portrait” spectra from the Magellan Inamori Kyocera Echelle spectrograph on the Magellan Clay Telescope at Las Campanas Observatory. The selected targets were identified as r-process-enhanced metal-poor stars in previous RPA snapshot analyses. They have also been linked to possible chemodynamically tagged groups, indicating that the stars may have formed in dwarf galaxies that were later accreted into the Milky Way halo. These stars have also been tentatively linked to the Thamnos structure. The detailed chemical abundances in this work confirm that 2MASS J14592981−3852558 and J15211026−0607566 are r-II stars, while 2MASS J19445483−4039459 is found to lie just below the threshold for r-I status. The r-II stars show signs of slight enhancement in fission fragments compared to 2MASS J19445483−4039459. Based on radioactive age dating with Th, the r-process material in the two r-II stars is found to be old (with ages > 10 Gyr); neither star shows signs of an actinide boost. The varying elemental compositions suggest that these stars likely did not originate in the same environment, though each could be consistent with originating in the Thamnos progenitor.