Phase I/II Study of CAR.70- Engineered IL15-transduced Cord Blood-derived NK Cells in Conjunction With Lymphodepleting Chemotherapy for the Management of Relapse/Refractory Hematological Malignances

The goal of this clinical research study is to learn about the safety of giving immune cells called natural killer (NK) cells with chemotherapy to patients with leukemia, lymphoma, or multiple myeloma. Immune system cells (such as NK cells) are made by the body to attack foreign or cancerous cells. Researchers think that NK cells you receive from a donor may react against cancer cells in your body, which may help to control the disease.

Inclusion criteria: 1. Patients with hematological malignances with an expression of CD70 in the pre-enrollment tumor sample ≥ 10% measured by immunohistochemistry or flow cytometry. 2. Patients must meet diseases specific eligibility criteria (see below) 3. Patients at least 1 week from last cytotoxic chemotherapy at the time of starting lymphodepleting chemotherapy, except for Hydroxyurea which is allowed for peripheral blood count control in AML, CML, and MDS patients until the day prior to administration of lymphodepleting chemotherapy. Patients may continue tyrosine kinase inhibitors or other targeted therapies until up to three days prior to administration of lymphodepleting chemotherapy. 4. Localized radiotherapy to one or more disease sites is allowed prior the infusion provided that there are additional disease sites that are not irradiated to assess response 5. Karnofsky Performance Scale \> 50% for patients who are \>16 years old or Lansky score ≥50% for patients who are ≤16 years of age. 6. Adequate organ function: 1. Renal: Serum creatinine \/= 30 ml/min/1.73 m2 2. Hepatic: ALT/AST \