This trial will be performed as a multi-center phase I/II trial with MB-CART2019.1 and consists of part I. In part I, 12 to 18 patients with relapsed or resistant CD20 and CD19 positive NHL/CLL/SLL will be treated. Six plus three (6+3) patients in dose level 1 and 2 will be treated.

The trial will be conducted in Hematology Departments of Hospitals which meet the structural and personnel requirements for performing the planned regular trial-related investigations. Only sites will be chosen with expertise in and necessary facilities for managing cytokine release storm and other severe adverse events associated with this therapy such as neurotoxicity. A corresponding training to site personnel prior to trial start must be performed. The responsible intensive care unit (ICU) must be informed about the clinical trial before inclusion of the first patient and the respective dosing date in order to make sure that the medical staff of the ICU is able to react appropriately without any loss of time in case of emergency. The University Hospital of Cologne will provide the Coordinating Investigator. Additional clinical sites may be added during the trial.

Patients will be screened between day -30 and day -15. If the patient satisfies all the protocol inclusion and none of the exclusion criteria, he/she will be included in the clinical trial. Leukapheresis will be performed at the collection center on day -14 according to local standard practice. The leukapheresis product of the patient will be shipped by a special courier to the designated manufacturing center assigned by the sponsor. The leukapheresis sample will be used for the individual manufacturing of MB-CART2019.1 by using the automated CliniMACS Prodigy® System. The manufacturing of MB-CART2019.1 will start on day -13 and will be finished on day -1.

On day 5 of the manufacturing process the IPC (in-process-control) will indicate, if the manufacturing process is successful. Therefore, the lymphodepleting chemotherapy must only be started after the positive result of the IPC was confirmed by the manufacturer. Chemotherapy for lymphodepletion will be done on days -5 to -3.

Administration of MB-CART2019.1 will be performed on day 0 in the Hematology Departments of all sites. Patients will be followed up as inpatients until week 4 with close monitoring of their vital functions and lab parameters for signs of adverse events. In the second follow-up phase (week 4 until week 12), response will be assessed, and adverse events will be documented. A follow-up examination will be performed at week 12 (achievement of primary endpoint) and at month 12 which is considered end of trial or end of active part of the trial. In the long-term follow-up yearly until 5 years or patient's death, safety and response assessment as well as persistence of MBCART2019.1 will be performed. These assessments will be analyzed and reported separately and are not part of the entire clinical trial. This is a 6+3 trial design with a 0.3 log dose increment (1x106/2.5x106 MBCART2019.1 per kg BW in a single infusion) and maximum 2 dose levels. If none or one of the six patients at dose level 1 experiences a dose limiting toxicity, another six patients will be treated at dose level 2. If two DLTs are observed at dose level 1 another three patients will be treated with the same dose. If more than two DLTs are observed at dose level 1, trial will continue at dose level 0. Dose escalation continues until at least \>2 patients among a cohort of six to nine patients experience dose-limiting toxicities or dose level 2 is completed. The MTD is defined as the dose level below the dose inducing a DLT in more than 2 patients within one dose level. DLT will be evaluated within 4 weeks after the infusion of MB-CART2019.1. An interval of at least 28 days between the treatment of the first and the second patient in each dose level is mandatory. An observation period for DLT of 28 days is considered to be safe to exclude potential toxicities prior to inclusion of the next patients into the same dose group or prior to dose escalation.