Allogeneic Natural Killer Cells in Patients With Recurrent Ovarian Cancer, Fallopian Tube, and Primary Peritoneal Cancer

Inclusion Criteria: * Diagnosis of recurrent ovarian cancer, fallopian tube, or primary peritoneal cancer who meets the following criteria: * Measurable disease (≥ 1 cm) per Response Evaluation Criteria for Solid Tumors (RECIST) - patients with bone as their only site of metastatic disease will not be eligible * Progression on or failure to respond to at least 2 salvage chemotherapy regimens (2 regimens given for disease recurrence) for recurrent/metastatic ovarian, fallopian tube, or primary peritoneal cancer * If history of brain metastases, stable for at least 3 months after treatment - A brain computed tomography (CT) scan will only be required in subjects with known brain metastases at the time of enrollment or in subjects with new clinical signs or symptoms suggestive of brain metastases. * Available related HLA-haploidentical natural killer (NK) cell donor (by at least class I serologic typing). If biologic parents or siblings are available, can proceed with work-up of subject prior to return of human leukocyte antigen (HLA) typing results. * Age 18 years or older * Gynecology Oncology Group (GOG) performance status 0 or 1 * Adequate organ function as determined by the following criteria within 14 days of study enrollment: * Bone marrow: platelets ≥ 80,000 x 10\^9/L and hemoglobin ≥ 9g/dL, unsupported by transfusions; absolute neutrophil count (ANC) ≥ 1000 x 10\^9/L, unsupported by granulocyte-colony stimulating factor (G-CSF) or granulocyte macrophage-colony stimulating factor (GM-CSF) * Renal function: creatinine (Cr) ≤ 2.0 mg/dL * Liver function: aspartate aminotransferase (AST), alanine aminotransferase (ALT), total bilirubin, alkaline phosphatase \< 5 times upper limit of institutional normal * Cardiac: Left ventricular ejection fraction \>40% * Pulmonary function: \> 50% corrected Carbon Monoxide Diffusing Capacity (DLCO) and Forced expiratory volume in one second (FEV1), if presence of pleural effusion due to metastatic disease \>40% corrected DLCO and FEV1 acceptable. * Able to be off prednisone or other immunosuppressive medications for at least 3 days prior to Day 0 * Voluntary written informed consent signed before performance of any study related procedure not part of normal medical care. Exclusion Criteria: * Pregnant or lactating - The agents used in this study may be teratogenic to a fetus and there is no information on the excretion of agents into breast milk. All females of childbearing potential must have a blood test or urine study within 14 days prior to registration to rule out pregnancy. * Active infection - subjects must be afebrile, off antibiotics, and with no uninvestigated radiologic lesions (infiltrates or lesions with negative cultures or biopsies are allowed). Human anti-mouse antibody (HAMA) monitoring: All subjects will be questioned about prior exposure to antibody therapy (including OKT3, Rituximab, Trastuzumab, etc). Responses will be recorded and reported to the FDA as part of the annual report. For subjects with no prior antibody therapy exposure, no further action will be taken. For subjects who have received previous antibody therapies 10 ml of serum (red top tube) will be drawn before starting therapy and banked per section 8.1. The presence of HAMA will not exclude a patient from the study.