A preparation of allogeneic, 'off-the-shelf' (OTS), universal transcription activator-like effector nuclease (TALEN)-engineered, gene-edited T-lymphocytes that have been transduced with a vector expressing a chimeric antigen receptor (CAR) containing a single chain variable fragment (scFv) derived from a monoclonal antibody specific for the human tumor-associated antigen (TAA) B-cell maturation antigen (BCMA; tumor necrosis factor receptor superfamily member 17; TNFRSF17), with potential immunostimulating and antineoplastic activities. Using TALEN technology, the T-cell receptor (TCR) alpha chain (TRAC) and CD52 genes are deleted from the CAR T-cells. Upon administration, the allogeneic anti-BCMA CAR-transduced T-cells ALLO-715 specifically recognize and induce selective toxicity in BCMA-expressing tumor cells. BCMA, a receptor for both a proliferation-inducing ligand (APRIL) and B-cell activating factor (BAFF), is a member of the tumor necrosis factor receptor superfamily (TNFRSF). BCMA is found on the surfaces of plasma cells, is overexpressed on malignant plasma cells and plays a key role in plasma cell proliferation and survival. Deletion of the CD52 gene makes the modified donor T-cells resistant to an anti-CD52 monoclonal antibody treatment, that is used during lymphodepletion. The knockout of TRAC eliminates TCR expression and is intended to abrogate the potential induction of graft-versus-host disease (GvHD) by the donor T-cells. The donor-derived, gene-edited CAR T cells have reduced production times and have increased availability when compared to autologous CAR-T cells, which use the patient's own cells and are produced on an individual basis. In addition, if the ALLO-715 cells cause unacceptable side effects, the incorporated CD20-based off-switch permits selective depletion of the ALLO-715 cells when the anti-CD20 monoclonal antibody rituximab is administered.