A Phase I/II Study of Combination Immunotherapy for Advanced Cancers Including HPV-Associated Malignancies, Small Bowel, and Colon Cancers

Background: * Although PD-1(L1) inhibitors have been approved for the treatment of over a dozen different tumor types in recent years, the majority of patients with advanced cancer still do not respond to these agents, including patients with microsatellite stable (MSS) colon cancer and patients with checkpoint refractory cancers (e.g., oropharyngeal, cervical). * Clinical studies suggest that treatment with a bifunctional fusion protein targeting PD-L1 and TGF beta (bintrafusp alfa) may help overcome resistance or refractoriness to anti PD-1(L1) therapy alone. * Preclinical and clinical studies suggest that treatment with a histone deacetylase inhibitor (HDAC inhibitor) concomitantly with anti PD-1(L1) therapy is safe and may help overcome resistance or refractoriness to anti PD-1(L1) therapy alone. * Preclinical and clinical studies suggest that treatment with a tumor targeted immunocytokine (PDS01ADC) concomitantly with anti PD-1(L1) therapy is safe and may help overcome resistance or refractoriness to anti PD-1(L1) therapy alone. * Preclinical studies suggest that the use of a combination of multiple immunotherapy agents may have improved anti-tumor efficacy. * Specifically, preclinical studies have shown that the combination of three immunotherapy agents (1) an HDAC inhibitor, entinostat (2) a tumor targeted immunocytokine (PDS01ADC), and (3) a bifunctional fusion protein targeting PD-L1 and TGF beta (bintrafusp alfa) produces greater anti-tumor activity than single or dual combinations of these agents. Objectives: * Phase I: To determine the recommended phase II dose (RP2D) of entinostat in combination with PDS01ADC and bintrafusp alfa. * Phase II: To evaluate the objective response rate (ORR) (PR+CR) according to Response Evaluation Criteria (RECIST 1.1) of the combination of entinostat, PDS01ADC, and bintrafusp alfa in two separate populations: * Checkpoint refractory human papillomavirus (HPV) associated malignancies; * MSS small bowel or colorectal cancer. Eligibility: * Age \>= 18 years old. * Phase I: Subjects with cytologically or histologically confirmed locally advanced or metastatic HPV associated malignancies or MSS small bowel or colorectal cancer (Cohort 1). * Phase II: Subjects with cytologically or histologically confirmed locally advanced or metastatic HPV associated malignancies (Cohort 2), or MSS small bowel or colorectal cancer (Cohort 3). * Prior first line systemic therapy is required unless the participant declines standard treatment after appropriate counseling has been provided. * Subjects must have measurable disease per RECIST 1.1. Design: * This is a phase I/II trial of combination immunotherapy. * Participants will be treated with a one week lead in of entinostat alone followed by the combination of entinostat, PDS01ADC and bintrafusp alfa (Arm 1 \& Arm 2). Up to 12 additional participants will be treated with a one week lead in of entinostat alone followed by the combination with PDS01ADC (without bintrafusp alfa, Arm 3). * Phase I (Arm 1): * Arm 1 will be conducted using dose escalation/de-escalation of entinostat and dose escalation of PDS01ADC with a fixed dose of bintrafusp alfa in Cohort 1 (up to 36 total). * Once the combination of all three agents has been determined to be safe, participants from Cohort 2 and Cohort 3 may enroll into -Phase II. * Phase II (Arm 2 and Arm 3): * (Arm 2) will be conducted using a Simon optimal two-stage design. * Cohort 2 (checkpoint refractory HPV associated malignancies, 16 total) and cohort 3 (MSS small bowel or colorectal cancer, 16 total) participants will each be enrolled to Arm 2. * If one or more out of twelve participants in a given cohort (2 or 3) has an objective response, accrual will be expanded to enroll 16 evaluable participants on that cohort. * If 3 or more of 16 (18.8%) participants respond in a given cohort-arm combination, that would be sufficiently interesting to warrant further study of the combination in later trials in that disease type. * Arm 3: Up to 12 additional participants with checkpoint refractory HPV associated cancer may enroll to the combination of entinostat plus PDS01ADC (without bintrafusp alfa).