Separation of single-chirality single-wall carbon nanotubes (SWCNTs) and their enantiomers holds significant potential for materials science and various applications but challenges in scalability and precision persist. In this study, we introduce a systematic approach to identify separation conditions for metallic SWCNTs in aqueous two-phase extraction (ATPE), precisely identifying improved conditions for isolating multiple armchair and chiral (n,m) species. We quantify these conditions by determining partition coefficient change condition (PCCC) values for both binary and ternary surfactant combinations. This information enables optimization for efficient separation of high-purity armchair nanotubes such as (6,6), (7,7), (8,8) and (9,9), and for isolation of enantiomeric nonarmchair nanotubes, including challenging metallic species such as the (8,5), (7,4), (9,3), (10,4) and (10,7). Lastly, separated single (n,m) populations are reseparated in ATPE at precise steps in both binary and ternary surfactant mixtures to resolve their enantiomers, extracting information on the underlying mechanism of metallic SWCNT ATPE and highlighting the utility of sodium cholate for achieving single enantiomer level separations.