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 limit normal (ULN). * Bilirubin less than or equal to 1.5 x ULN. * Serum glutamic oxaloacetic transaminase (SGOT) less than or equal to 3 x ULN. * Alkaline phosphatase less than or equal to 3 x ULN. * Participant or legal representative must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure. * Female subjects must either be of non-reproductive potential (i.e., post-menopausal by history: \>= 50 years old and no menses for \>= 1 year without an alternative medical cause; OR history of hysterectomy, OR history of bilateral tubal ligation, OR history of bilateral oophorectomy) or must have a negative urine or serum pregnancy test within 28 days of study treatment, confirmed prior to treatment. * Patients must have an Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1. Exclusion Criteria: * Metastatic disease to the central nervous system and any site above diaphragm. * Other serious illnesses (e.g., serious infections requiring antibiotics \[with the exception of uncomplicated UTI\], bleeding disorders). * Chemotherapy, radiation therapy, or immunotherapy within 4 weeks prior to first dosing of study agent. Concomitant hormonal therapies are allowed. * Patients who have an active autoimmune disease (e.g., rheumatoid arthritis, systemic lupus erythematosus \[SLE\], ulcerative colitis, Crohn's Disease, multiple sclerosis \[MS\], ankylosing spondylitis) requiring chronic use of steroids or other immunosuppressives. * Patients being chronically treated with immunosuppressive drugs such as cyclosporin, adrenocorticotropic hormone (ACTH), or systemic chronic corticosteroids. NOTE: Recent or current use of inhaled steroids is not exclusionary. * Use of chronic corticosteroids, hydroxyurea, or immunomodulating agents (e.g., interleukin 2, interferon alpha or gamma, granulocyte colony stimulating factors, etc.) within 30 days prior to study entry. * NOTE: Recent or current use of inhaled steroids is not exclusionary. If subjects are prescribed a brief course of oral steroids, the use should be limited to less than 7 days. Use of steroids before apheresis and immune assessment blood draws will affect white blood cell function (wash out period of 1 week). * Patients with a known immunodeficiency disease including cellular immunodeficiencies, hypogammaglobulinemia or dysgammaglobulinemia; patients who have acquired, hereditary, or congenital immunodeficiencies. Specific testing is not required, however may be done as clinically indicated. * Patients with uncontrolled diseases other than cancer may be excluded if after consultation with PI and research team it is decided it might affect the treatment efficacy or toxicity.. * Patients with tumors of low malignant potential, except ovarian pseudomyxoma or with no peritoneal disease at initial diagnosis. * Patients with a history of other invasive malignancies, with the exception of nonmelanoma skin cancer, are excluded if there is any evidence of other malignancy being present within the last three years. Patients are also excluded if their previous cancer treatment contraindicates this protocol therapy. * Evidence of current drug or alcohol abuse or psychiatric impairment, which in the investigator's opinion will prevent completion of the protocol therapy or follow-up. Specific testing is not required, however may be done as clinically indicated. * Any condition that in the opinion of principal investigator (PI) would preclude patient from successfully completing the protocol therapy or follow-up.