A preparation of T-lymphocytes transduced with a lentiviral vector expressing a compound chimeric antigen receptor (cCAR) containing two distinct units of CARs, one specific for the tumor-associated antigen (TAA) cluster of differentiation 20 (CD20) and one specific for the TAA CD19, with potential immunomodulating and antineoplastic activities. Upon administration, the CD20-CD19 cCAR T cells specifically and simultaneously target and bind to tumor cells expressing CD20 and/or CD19. This induces selective toxicity in tumor cells that express CD20 and/or CD19. Both CD19 and CD20 are B-cell-specific cell surface antigens overexpressed in B-cell lineage malignancies. Targeting two different antigens may improve coverage and protect against antigen escape and relapse as it is less likely for tumor cells to lose both antigens.