Atezolizumab, Guadecitabine, and CDX-1401 Vaccine in Treating Patients With Recurrent Ovarian, Fallopian Tube, or Primary Peritoneal Cancer

PRIMARY OBJECTIVES: I. To determine the safety of fixed doses of atezolizumab (MPDL3280A) in combination with guadecitabine (SGI-110). (Phase I) II. To evaluate toxicity of the combination as defined by National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version 5.0. (Phase I) III. To study if SGI-110 improves the benefit of atezolizumab and then if the further addition of the DEC-205/NY-ESO-1 fusion protein CDX-1401 (CDX-1401)/poly ICLC adds further clinical benefit by analyzing progression free survival (PFS), using Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria. (Phase IIb) SECONDARY OBJECTIVES: I. To observe and record anti-tumor activity. (Phase I) II. To determine overall survival (OS), objective response rate (complete and partial responses), clinical benefit rate (response + stable disease), CA-125 reduction (percentage of patients with CA-125 reduction by \>= 50%), and duration of response. (Phase IIb) III. To assess the impact of the combination of atezolizumab, SGI-110, and CDX-1401 on anti-tumor immune responses. (Phase IIb) IV. To assess the impact of SGI-110 on NY-ESO-1 expression in tumor tissue. (Phase IIb) V. To assess toxicities associated with the combination cohorts (2 and 3), as there is little human experience with these combinations. (Phase IIb) EXPLORATORY/TRANSLATIONAL OBJECTIVES: I. To determine the effectiveness of SGI-110 on enhancing vaccine efficacy by assessing NY ESO 1 specific cellular and humoral immunity. Ia. Peripheral blood NY ESO 1 specific CD8+ and CD4+ T cells. Ib. Peripheral blood NY ESO 1 specific antibodies. Ic. Peripheral blood unrelated CTA specific antibodies (antigen spreading). Id. Peripheral blood frequency of CD4+CD25+FOXP3+ regulatory T cells. Ie. Examine potential differential effect of NY-ESO-1 expression on PFS. II. To assess the impact on PDL1 expression in tumor tissue. III. Evaluation of therapeutic efficacy on immune cell phenotype. IV. Deoxyribonucleic acid (DNA) methylation and DNA methylome: in pre- and on-treatment peripheral blood, serum (circulating DNA), and tumor biopsies. V. Pre-and on-treatment density and location of tumor infiltrating CD3+ and CD8+ T cells. VI. Evaluate the pre- and post-treatment mutational and neo-antigen load and therapeutic efficacy. VII. Pre- and post-treatment T cell receptor (TCR) repertoire to study the effect of TCR V beta diversity due to combination of PDL1 blockade, epigenetic modification, and vaccination on therapeutic efficacy. VIII. Gut microbiota at baseline and one on-treatment sample at C4D1 (cycle 4, day 1) or at progression, whichever is earlier to evaluate the role of microbiota on the therapeutic efficacy of the proposed combination therapy. OUTLINE: This is a phase I, dose-escalation study of guadecitabine followed by a phase IIb study. Patients are randomized to 1 of 3 cohorts. COHORT I: Patients receive atezolizumab intravenously (IV) over 30-60 minutes on days 1 and 15. Treatment repeats every 28 days for up to 24 courses in the absence of disease progression or unacceptable toxicity. COHORT II: Patients receive guadecitabine subcutaneously (SC) on days 1-5. Treatment repeats every 28 days for up to 6 courses in the absence of disease progression or unacceptable toxicity. Patients also receive atezolizumab IV over 30-60 minutes on days 8 and 22. Treatment repeats every 28 days for up to 24 courses in the absence of disease progression or unacceptable toxicity. COHORT III: Patients receive guadecitabine and atezolizumab as in Cohort II. Patients also receive CDX-1401 vaccine IV on day 15 and poly ICLC SC on days 15-16. Treatment repeats every 28 days for up to 6 courses in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up at 30 days and then every 2 months for up to 1 year.