This is an open-label, non-randomized study to evaluate the safety of two planned infusions of BPX-501 T cells after partially mismatched, related (haploidentical) HSCT in adults with hematologic malignancies.

The objective is to evaluate the safety of two planned infusions of BPX-501 after partially mismatched, related HSCT with post-transplant cyclophosphamide and to evaluate the safety and efficacy of the treatment of dimerizer drug, rimiducid (AP1903), to subjects who received BPX-501 and have uncontrolled GvHD. Assuming no toxicity, enrollment will proceed sequentially for the initial 9 patients (following the 3+3 design), who will be followed for 100 days, prior to enrolling the subsequent 31 patients. Toxicity may increase the number of initial group of patients). As multiple dose levels may be administered among the first 9 (or more) patients, toxicity will be assessed on the cohort with the maximum tolerated dose (MTD).

The Medical Monitoring committee will review the data with the investigators and determine whether to proceed and or implement any changes to the protocol

BPX-501 contains genetically modified donor T cells that have an inducible safety switch iCasp9 suicide gene. In the event of acute GvHD, administration of rimiducid dimerizes and activates caspase 9; this activates downstream caspases, obligating cellular apoptosis within 24 hours.

Inclusion Criteria:

1. Signed informed consent

2. Patients with one of the life-threatening hematological malignancies:

   • Acute lymphocytic leukemia (ALL) in CR1 with high-risk features including adverse cytogenetics such as t(9;22), t(1;19), t(4;11), or MLL gene rearrangements; greater than 1 cycle to achiever remission or with persistent MRD; ALL in second or greater remission with or without MRD. Acute myeloid leukemia (AML) in CR1 with high-risk features defined as: Greater than 1 cycle of induction therapy required to achieve remission; Preceding myelodysplastic syndrome (MDS) or myeloproliferative disease; Presence of FLT3 mutations or internal tandem duplications; FAB M6 or M7 classification; Adverse cytogenetics, -5, del 5q, -7, del7q, abnormalities involving 3q, 9q, 11q, 20q, 21q, 17, +8 [> 3 abnormalities];
   • AML in second or greater remission, primary induction failure and patients with relapsed disease;
   • Advanced chronic myeloid leukemia (CML) who have progressed to blast phase or accelerated phase and are in need of a transplant and do not have an HLA matched donor;
   • MDS with IPSS intermediate-2 or higher or therapy-related MDS.Hodgkin lymphoma or Non-Hodgkin lymphoma (NHL): relapsed disease where remission duration is less than 1 year, relapse after previous autologous transplant, or failure to achieve CR with chemotherapy.

3. Age ≥ 18 years and ≤ 65 years

4. Deemed eligible for allogeneic stem cell transplantation

5. Lack of suitable conventional donor (i.e. 8/8 related or unrelated donor) or presence of rapidly progressive disease not permitting time to identify an unrelated donor

6. HLA typing will be performed at high resolution (allele level) for the HLA-A, -B, Cw, and DRBl loci

   • A minimum genotypic identical haplotype match of 4/8 is required
   • The donor and recipient must be identical, as determined by high resolution typing, at least one allele of each of the following genetic loci: HLA-A, HLA-B, HLA-Cw, and HLA- DRB1

7. Subjects with adequate organs function as measured by:

   • Cardiac: Left ventricular ejection fraction at rest must be >45%
   • Pulmonary: FEV 1, FVC, DLCO (diffusion capacity) > 50% predicted (corrected for hemoglobin); or O2 saturation > 92% on room air
   • Hepatic: Direct bilirubin ≤ 3 x upper limit of normal (ULN), or AST/ALT ≤ 5 x ULN
   • Renal: Serum creatinine within normal range for age or creatinine clearance, or with a recommended GFR ≥ 50 mL/min/1.73m2

8. Performance status: Karnofsky ≥ 80%

Exclusion Criteria:

1. HLA 8/8 allele matched (HLA-A,-B,-Cw,-DRBl) related or unrelated donor able to donate;
2. Autologous hematopoietic stem cell transplant ≤ 3 months prior to enrollment;
3. Prior allogeneic transplantation;
4. Active CNS involvement by malignant cells (less than 2 months from the conditioning);
5. Current uncontrolled bacterial, viral or fungal infection (currently taking medication with evidence of progression of clinical symptoms or radiologic findings); the PI is the final arbiter of this criterion;
6. Positive HIV serology or viral RNA (≥ Grade III per CTCAE criteria);
7. Pregnancy (positive serum or urine βHCG test) or breast-feeding;
8. Fertile men or women unwilling to use effective forms of birth control or abstinence for a year after transplantation;
9. Bovine product allergy.
10. Severe obesity (patient's weight is >/= 1.5x the donor weight).