Specialized Immune Cells (nCTLs) and a Vaccine (Alpha-type-1 Polarized Dendritic Cells) in Treating Patients With Stage II-IV Ovarian, Fallopian Tube, or Primary Peritoneal Cancer

Inclusion Criteria: * Eligible patients will be women with stages II-IV epithelial ovarian, fallopian tube, or primary peritoneal carcinoma with no radiologic evidence of disease (NED) or minimal disease burden after 1st line therapy. These patients would normally enter a period of observation after standard management. * Life expectancy \> 6 months. * Have been informed of other treatment options. * Patients must be reasonable candidates for intraperitoneal (IP) port placement with no prior evidence of persistent abdominal wall or intraperitoneal infections, renal toxicity, or bowel obstruction or fistula. * Patients must have documented available tumor: at least 1 cm of bulk tumor mass collected at the time of primary or interval debulking surgery. The specimen may be obtained on this protocol or as part of other Institutional Review Board (IRB) approved tumor banking protocols. * Patients should be free of active infection requiring antibiotics (with the exception of uncomplicated urinary tract infection \[UTI\]). * Must have adequate venous access for apheresis. (Pheresis catheter placement for cell collection is allowed). * Patient must agree to leukapheresis. * Patients must agree to appropriate clinical monitoring to receive the study regimens. * Absolute neutrophil count (ANC) greater than or equal to 1,000/uL. * Platelets greater than or equal to 75,000/uL. * Hemoglobin greater than or equal to 8.0 g/dL. * Creatinine less than or equal to 2 x institutional upper lim…