IP ALT-803 Followed by SQ ALT-803 for Ovarian Cancer

Inclusion Criteria * Diagnosis of FIGO stage III or grade IV epithelial ovarian, fallopian tube or primary peritoneal carcinoma, has received at least 3 cycles of first line IV/IP cisplatin and paclitaxel chemotherapy and has stable disease or better - refer to Appendix II for FIGO staging system (Note: to be eligible for this study, the patient must receive a minimum of 3 cycles of IP therapy; however, patients may continue on IV only 1st line therapy for additional cycles as long as inclusion criteria 4.1.2 is met) * Able to begin study therapy within 3 months of final dose of first line chemotherapy * Functioning intraperitoneal catheter * ≥ 18 years of age * GOG performance status ≤ 2 (Appendix II) * Adequate organ function within 14 days of enrollment defined as: * Hematology: hemoglobin ≥ 8 g/dl, absolute neutrophil count (ANC) ≥ 1500/ul, platelets ≥ 50 x 109/L * Creatinine: ≤ 2.0 mg/dL * Hepatic: SGOT and SGPT ≤ 3 x upper limit of institutional normal (ULN) * Ability to be off prednisone and other immunosuppressive drugs for at least 3 days prior to and while receiving ALT-803 * Voluntary written consent prior to the performance of any research related procedures Exclusion Criteria * Received any investigational agent within the 14 days before the start of ALT-803 * Class II or greater New York Heart Association Functional Classification criteria (Appendix II) or serious cardiac arrhythmias likely to increase the risk of cardiac complications of cytokine therapy (e.g. ventricular tachycardia, frequent ventricular ectopy, or supraventricular tachyarrhythmia requiring chronic therapy) * Marked baseline prolongation of QT/QTc interval (e.g. demonstration of a QTc interval greater than 500 milliseconds) * Uncontrolled bacterial, fungal or viral infections including HIV-1/2 or active hepatitis C/B - chronic asymptomatic viral hepatitis is allowed * Active autoimmune disease requiring systemic immunosuppressive therapy * History of severe asthma and currently on chronic systemic medications (mild asthma requiring inhaled steroids only is eligible) * Uncontrolled hypertension: defined as ≥2 readings over 160 mmHg systolic or 110 mmHg diastolic within month prior to enrollment despite optimal anti-hypertensive medication. Patients with high readings which improve to ≤160/110 after adjustment of medications will be eligible. * History of pulmonary disease or abnormal pulmonary function studies * History of narcolepsy or any neurological condition which may impair consciousness