Purpose

This study will be separated into 3 distinct phases designated as the Phase 1 study, Phase 2 pivotal study (Cohort 1 and Cohort 2), and Phase 2 safety management study (Cohort 3 and Cohort 4, Cohort 5 and Cohort 6). The primary objectives of this study are: - Phase 1 Study: Evaluate the safety of axicabtagene ciloleucel regimens - Phase 2 Pivotal Study; Evaluate the efficacy of axicabtagene ciloleucel - Phase 2 Safety Management Study: Assess the impact of prophylactic regimens or earlier interventions on the rate and severity of cytokine release syndrome (CRS) and neurologic toxicities Subjects who received an infusion of KTE-C19 will complete the remainder of the 15 year follow-up assessments in a separate long-term follow-up study, KT-US-982-5968.