The clinical use of chimeric antigen receptor (CAR) T-cell therapy is growing rapidly due to expanding indications for standard of care treatment and the development of new investigational products. The establishment of consensus diagnostic criteria for cytokine release syndrome (CRS) and immune effector cell associated neurotoxicity syndrome (ICANS), alongside the steady use of both tocilizumab and corticosteroids for treatment, have been essential to facilitating the widespread use. Pre-emptive interventions to prevent more severe toxicities has improved safety, facilitating CAR T-cell therapy in medically frail populations and those at high-risk of severe CRS/ICANS. Nonetheless, the development of persistent or progressive CRS and ICANS remains problematic, as it impairs patient outcomes and is challenging to treat. In this case-based discussion, we highlight a series of cases of CRS and/or ICANS refractory to front-line interventions. We discuss our approach to managing refractory toxicities that persist or progress beyond initial tocilizumab or corticosteroid administration, delineate risk-factors for severe toxicities, highlight the emerging use of anakinra, and review mitigation strategies and supportive care measures to improve outcomes in patients who develop these refractory toxicities.