Feasibility and Safety of Collecting and Combining Autologous Hematopoietic Stem Cells With Chimeric Antigen Receptor (CAR) T-Cell Therapy in Subjects With Relapsed/Refractory Hematological Malignancies

Inclusion Criteria:

* Age 18 - 85 years.
* Histologically proven hematological malignancy according to the World Health Organization 2016 classification criteria for which a commercially available, FDA-approved CAR T product exists.
* Relapsed or refractory disease, defined by the following:

  * Disease progression after last regimen, or
  * Refractory disease: failure to achieve a partial response (PR) or complete remission (CR) to the last regimen
* At least 2 weeks or 5 half-lives, whichever is shorter, must have elapsed since any prior systemic therapy for the malignancy at the time the subject is planned for leukapheresis.
* Toxicities due to prior therapy must be stable or recovered to ≤ Grade 1 with the exception of alopecia.
* Subjects with an active uncontrolled infection should not start CAR T treatment until the infection has resolved.
* Eastern cooperative oncology group (ECOG) performance status 0 - 2.
* Adequate hematologic, hepatic, and cardiac function
* Serum pregnancy test for women of childbearing potential (WOCBP) at Screening.
* Willing to comply to research specimen collection as specified in the protocol.
* Written informed consent obtained from subject and ability for subject to comply with the requirements of the study.

Exclusion Criteria:

* Autologous hematopoietic cell transplant intent or execution within 8 weeks of planned CAR T infusion.
* History of allogeneic cell transplantation within 8 weeks of planned CAR T infusion.
* Presence or suspicion of fungal, bacterial, viral, or other infection that is uncontrolled or requiring IV antimicrobials for management at time of screening.
* History of myocardial infarction, cardiac angioplasty or stenting, unstable angina, or other clinically significant cardiac disease within 6 months of enrollment.
* History of a seizure disorder, cerebrovascular ischemia/hemorrhage, dementia, or any autoimmune disease with CNS involvement.
* Doses of corticosteroids of greater than or equal to 5 mg/day of prednisone or equivalent doses of other corticosteroids and other immunosuppressive drugs are not allowed prior to enrollment. A washout period of 10 days prior to leukapheresis and 10 days prior to anti-CD19 CAR T cell administration is required.
* Any medical condition likely to interfere with assessment of feasibility or safety of study treatment.
* Live vaccine ≤ 6 weeks prior to planned start of conditioning regimen.
* History of severe immediate hypersensitivity reaction to any of the agents used in this study.
* Current pregnancy or breastfeeding because of the potentially dangerous effects of the preparative chemotherapy on the fetus or infant.
* Subjects of both sexes who are not willing to practice birth control from the time of consent through 6 months after the completion of conditioning chemotherapy. Females who have undergone surgical sterilization or who have been postmenopausal for at least 1 year are not considered to be of childbearing potential.
* In the investigator's judgment, the subject is unlikely to complete all protocol-required study visits or procedures, including follow-up visits, or comply with the study requirements for participation.
* Patients with obvious myeloid clonal hematopoiesis on the screening bone marrow biopsy will be excluded based on the risk of developing myeloid neoplasms with aHSC infusion.