Antiminor Histocompatibility Complex (MiHA) T Cells for Patients With Relapsed Hematologic Malignancies Following Matched HSCT (Guided Lymphocyte Immunopeptide Derived Expansion)

Inclusion Criteria: * Prior allogeneic HLA-matched stem cell transplantation * Any of the following hematologic malignancies: * Acute myeloid leukemia (AML) * Acute lymphoblastic leukemia (ALL) * Biphenotypic leukemia * Chronic lymphoblastic leukemia (CLL) * Hodgkin Lymphoma * Non-Hodgkin Lymphoma (NHL) * Multiple Myeloma (MM) * Myelodysplastic syndrome (MDS) * Presence of HLA2:01 and / or HLA44:02 and / or HLA-B\*44:03, HLA-A\*01:01; HLA-A\*03:01; HLA-A\*11:01;HLA A\*24:02; HLA-A\*29:02; HLA-A\*32:01; HLA-B\*07:02; HLA-B\*08:01; HLA B\*13:02; HLA-B\*14:02; HLA-B\*15:01; HLA-B\*18:01; HLA-B\*27:05; HLA B\*35:01; HLA-B\*40:01; or HLA-B\*57:01 * At least 6 months after allogeneic hematopoietic stem cell transplantation * Presence of detectable malignant disease post-transplantation in the form of molecular, cytogenetic or hematologic relapse of the malignant disorder. * Eligible to receive cytoreductive chemotherapy * Original stem cell donor available for leukocyte donation. * ECOG performance status ≤2. * Ability to provide written consent. * Accessible for treatment and follow up. * Presence of a targetable MiHA based on exome sequencing of the patient and donor Exclusion Criteria: * Active acute GVHD \> grade I * Prior grade III-IV acute GVHD within the last year * Uncontrolled chronic GVHD * Prior administration of donor lymphocyte infusion (DLI) * Use of T-cell depleting antibodies in the previous 30 days * Treatment with immune suppressors (oral or parenteral steroids corresponding to a dose of prednisone greater than 7.5 mg/day, calcineurine inhibitors, rapamycin, mycophenolate mofetil, etc) during the last 30 days. * Uncontrolled active infection * Uncontrolled central nervous system involvement by leukemia cells (blasts). * AST or ALT \> 2.5 x ULN (CTCAE grade 2) * Bilirubin \> 1.5 x ULN (CTCAE grade 2) * Creatinine clearance \< 50 mL/min * Positive test for human immunodeficiency virus (HIV) * Positive pregnancy test (women of childbearing age only) * Lactating women: the safety of this therapy on breast milk is not known. * Estimated probability of surviving less than 3 months * Known allergy to any of the components of GLIDE (e.g., dimethyl sulfoxide) * Intercurrent illness or medical condition precluding safe administration of the planned protocol treatment or required follow-up.