Bispecific CAR T Cells for B-cell Malignancies (BaseCAR-01 Trial)

Inclusion Criteria: * Age ≥ 18 years * Diagnosis of B-cell NHL or B-ALL with relapsed, refractory disease and no available standard therapeutic options (including commercially accessible CAR T products), including: * Acute B-lymphoblastic leukaemia * Burkitt lymphoma * Primary CNS lymphoma * DLBCL or high-grade lymphoma of any subtype * Primary mediastinal B cell lymphoma (including grey zone lymphoma) * Mantle Cell lymphoma * Low-grade B-cell NHLs: Follicular lymphoma, chronic lymphocytic leukaemia (CLL)/ small lymphocytic lymphoma (SLL), marginal zone lymphoma, hairy cell leukaemia, splenic B-cell lymphoma/leukaemia with prominent nucleoli, and lymphoplasmacytic lymphoma * CD19 and/or CD20 positive disease on most recent evaluation (by immunohistochemistry or flow cytometry) * ECOG clinical performance status ≤2 * Able to provide written informed consent. * Adequate organ function and bone marrow reserve, unless clearly caused by lymphoma and considered reversible, defined as: * Adequate hepatic function: Aspartate Aminotransferase (AST) and Alanine Aminotransferase (ALT) ≤3.0 × (ULN) and serum bilirubin ≤2.0 × ULN (except in congenital hyperbilirubinemia, such as Gilbert syndrome, where direct bilirubin ≤3.0 × ULN is allowed) * Adequate renal function: creatinine clearance ≥30 mL/min/1.73 m2 * Adequate pulmonary function: Forced Expiratory Volume in 1 second (FEV1) ≥50% (with adequate compliance) and pulse oxygenation \> 91% with room air. * Adequa…