Brief Summary: The purpose of this study is to determine the response rate to the combination of folate receptor alpha dendritic cells (FRaDCs) plus pembrolizumab in patients with advanced ovarian, fallopian tube, or primary peritoneal cancer. Vaccines made from a person's peptide treated white blood cells may help the body build an effective immune response to kill tumor cells.

Detailed Description: PRIMARY OBJECTIVES: I. To determine whether the combination of FRalphaDCs and pembrolizumab has an acceptable toxicity profile in patients with recurrent ovarian cancer (OC). (Phase I) II. To measure the confirmed objective response rate (ORR) to the combination of FRalphaDCs and pembrolizumab in patients with recurrent OC. (Phase II) SECONDARY OBJECTIVES: I. To estimate the disease control rate (DCR-percentage of patients achieving a complete response, partial response, or stable disease) of the combination of FRalphaDCs and pembrolizumab in patients with recurrent OC. II. To estimate the duration of response (DoR) in patients with recurrent OC treated with the combination of FRalphaDCs and pembrolizumab. III. To estimate the progression-free survival (PFS) of patients with recurrent OC treated with the combination of FRalphaDCs and pembrolizumab. IV. To estimate the overall survival (OS) of patients with recurrent OC treated with the combination of FRalphaDCs and pembrolizumab. 2.25 To characterize the adverse event (AE) profile in patients with recurrent OC treated with the combination of FRalphaDCs and pembrolizumab. CORRELATIVE OBJECTIVES: I. To determine whether the combination of FRalphaDCs and pembrolizumab induces an increase in the frequency of FRalpha-specific IL-17-secreting T cells (Th17s) in patients with recurrent OC. II. Characterize the T cell and antibody responses to FRalpha and assess the association between the emergence of immunity and recurrence-free (RFS). III. To determine whether the combination of FRalphaDCs and pembrolizumab induces an increase in the frequency of FRalpha-specific IFNgamma-secreting T cells (Th1s) in patients with recurrent OC. IV. To determine whether the combination of FRalphaDCs and pembrolizumab induces an increase in the frequency of FRalpha-specific IgG antibodies in patients with recurrent OC. V. To determine whether the combination of FRalphaDCs and pembrolizumab induces changes in the immune microenvironment of ovarian tumors. OUTLINE: Patients undergo apheresis for multi-epitope folate receptor alpha-loaded dendritic cell vaccine manufacturing on study. Patients then receive multi-epitope folate receptor alpha-loaded dendritic cell vaccine intradermally (ID) and pembrolizumab intravenously (IV) on study. Patients also undergo computed tomography (CT) and/or magnetic resonance imaging (MRI) as well as blood sample collection throughout the trial. Patients undergo biopsy on study. Patients are followed up at 90 days after last dose, every 3 months until 24 months after registration or until progression of disease, and then every 6 months up to 5 years after registration.