Study to Evaluate the Role of Siltuximab in Treatment of Cytokine Release Syndrome (CRS) and Immune Effector Cell Associated Neurotoxicity (ICANS) Related to CAR-T Cell Therapy

This study will evaluate the use of siltuximab to decrease the severity of cytokine release syndrome (CRS) and immune effector cell-associated neurological syndrome (ICANS) in patients who will receive chimeric antigen receptor (CAR) T-cell therapy for the treatment of hematological malignancies.

Inclusion Criteria: * Patients who are planned to receive chimeric antigen receptor T-cell therapy as per the United States Food and Drug Agency (USFDA) approved indications for Diffuse large B-cell lymphoma (DLBCL), Mantle cell lymphoma (MCL), Follicular lymphoma (FL), Primary mediastinal large B-cell lymphoma (PMBCL), High grade B-cell lymphoma, DLBCL arising from follicular lymphoma, Multiple myeloma and B-cell precursor acute lymphoblastic leukemia * Patients with hepatitis C virus (HCV) can be included if they have completed therapy for hepatitis C with undetectable HCV RNA viral load. * Patients with Hepatitis B can be included if they are on suppressive therapy for hepatitis B infection and with no detectable viral load. * Adequate organ function as defined below unless attributed to disease involvement.Acceptable window for assessing adequate organ function is 7 days to 30 days before planned CAR T-cell infusion with day 0 as the planned day of CAR T-cell infusion.Adequate liver function (bilirubin \< 2mg/dL, aspartate aminotransferase (AST) and/or alanine aminotransferase (ALT) \ 30ml/min using Cockcroft-Gault, based on actual weight) and adequate hematological parameters (Absolute neutrophil count ≥ 1,000/µL, Hemoglobin \> 8, Platelet Count ≥ 50,000/ µL) * Patients able to tolerate washout periods for therapies prior to CAR T-cell infusion. Systemic therapy: Washout period is 2 weeks prior to CAR T-cell infusion. Radiation therapy: Washout period is 1 week prior to CAR T-cell infusion. Corticosteroids: The washout period is 5 days prior to CAR T-cell infusion. * A negative urine pregnancy test is required within 1 week for all women of childbearing potential prior to enrolling on this trial. * For females of reproductive potential: use of highly effective contraception for at least 1 month prior to screening and agreement to use such a method during study participation and for an additional 4 months after infusion of siltuximab. * For males of reproductive potential: use of condoms or other methods to ensure effective contraception with partner * Willing and able to participate in all required evaluations and procedures in this study protocol including receiving intravenous administration of the investigational product and being admitted, when required, for at least 24 hours during investigational product administration. Exclusion Criteria: * Subjects requiring ongoing daily corticosteroid therapy at a dose of \> 10 mg of prednisone per day (or equivalent). Pulsed corticosteroid use for disease control is acceptable. * Active autoimmune disease requiring immunosuppressive therapy is excluded unless discussed with the principal investigator (PI) * Pregnant women are excluded from this study. * Evidence of ongoing systemic bacterial, or fungal or viral infection, except localized fungal infection of skin or nails. * Patients with ongoing or past HIV infection.