Study of Allo-QuadCAR01-T, an Allogeneic CAR-T Targeting CD19/CD20, in Patients With Relapsed or Refractory B-Cell Malignancies

This study is testing Allo-QuadCAR01-T, an off-the-shelf CAR-T cell therapy that targets two proteins (CD19 and CD20) found on cancer cells, in patients with relapsed or refractory B-cell blood cancers. **You may be eligible if...** - You are 18 or older - You have been diagnosed with relapsed or refractory B-cell non-Hodgkin's lymphoma (B-NHL) or chronic lymphocytic leukemia (CLL) - You have received at least 2 prior lines of treatment - Your performance status is 0 or 1 (able to carry out normal daily activities) - Your heart, liver, and kidneys are functioning adequately - Your tissue type (HLA) matches the donor cell product **You may NOT be eligible if...** - Your cancer has spread to the central nervous system (in early dose-escalation cohorts) - You received another CAR-T therapy within the past 3 months or had a severe immune reaction to prior CAR-T - You had an autologous stem cell transplant within the past 3 months - You have had a prior allogeneic stem cell transplant or solid organ transplant - You previously received a dual CD19/CD20 CAR-T therapy Talk to your doctor to see if this trial is right for you.