CAR T cell therapy achieves high degrees of success with respect to complete response and overall response rates in many hematological cancers, especially lymphomas. Compared to other immunotherapies, these "activated" blood products are plagued by a high incidence of a severe systemic inflammatory response syndrome, resulting from the exaggerated release of cytokines, chemokines, and other pro-inflammatory protein and lipid mediators. These can produce what is known as the "cytokine release syndrome" (CRS), associated with significant morbidity and mortality. Although successful CAR T cell therapy reduces the tumor load, the killing of large numbers of cancer cells and the persistence of apoptotic cellular debris within the tumor microenvironment (TME) may also be tumorigenic. We propose a single active pharmaceutical ingredient (API), the highly polyunsaturated omega-3 fatty acids eicosapentaenoic and docosahexaenoic acids, applying a refined and enriched fish oil, with multiple therapeutic targets that can be administered in precise doses. First, they rapidly modulate the intensity of the systemic inflammatory response, by modifying eicosanoid metabolism via intravenous administration. Second, as substrates for the production of specialized pro-resolving mediators (SPMs) of inflammation, they can help clear cellular debris within the TME, perhaps reducing the risks of new tumor formation. The employment of such a drug either in a prophylactic and/or a treatment manner might further improve the outcome of CAR T cell therapy.