The study population is advanced gastric, gastroesophageal, and esophageal adenocarcinoma participants who have failed upfront standard of care chemotherapy. The goal is to demonstrate that Rucaparib plus Ramucirumab with or without Nivolumab has a higher response rate than what has been reported for Ramucirumab in previously treated patients. Trial will be a phase 1/2 trial. The Phase 1 portion will determine the recommended Phase 2 treatment dose for the combination of Rucaparib plus Ramucirumab and Nivolumab and enroll approximately 6-9 participants. The Phase 2 portion of the study will involve 52 participants allocated between two treatment groups comparing Rucaparib plus Ramucirumab with or without Nivolumab. The participants will be selected based on the results of a screening HRD gene panel.

Inclusion Criteria:

• Half of the study population in phase 2 must have a deleterious tumor alteration in at least one protocol specified gene
• Gastric or gastroesophageal junction adenocarcinoma
• Advanced stage 4 or locally unresectable stage 3 disease
• Must have measurable disease
• Must consent to have a biopsy if archival tissue is not available or not enough for molecular testing
• Must show evidence of progression or intolerance to at least one previous standard of care systemic therapy (not more than 2 lines of prior therapy)
• Patients with human epidermal growth factor receptor 2 (HER2) positive disease must show progression on prior HER2 targeted therapy
• Toxicities related to prior treatment should be recovered to baseline or less than grade 2 according to CTCAE
• Adequate organ and marrow function
• Absence of active autoimmune disease that has required systemic treatment in the past 2 years
• Absence of conditions requiring systemic treatment with either corticosteroids or other immunosuppressive medications within 14 days of study drug administration. 10mg or less of prednisone or equivalent is acceptable
• Evidence of post-menopausal status or negative serum pregnancy test for female pre-menopausal patients
• Women of child-bearing potential and men with partners of child-bearing potential must agree to practice sexual abstinence, or to use two forms of adequate contraception prior to study entry, for the duration of study participation, and for 6 months following completion of therapy
• Men of child-bearing potential must not father a child or donate sperm while on this study and for 7 months after their last study treatment

Exclusion Criteria:

• Prior treatment with a programmed cell death protein 1 (PD1) or programmed death- ligand 1 (PD-L1) inhibitors

• Prior treatment with poly-(ADP-Ribose)polymerase (PARP)

• Patients with microsatellite instability (MSI) high or mismatch repair (MMR) deficient tumors

• Abdominal fistula, GI perforation, bowel obstruction, or intra-abdominal abscess within 6 months before first dose

• Evidence of active peptic ulcer disease, inflammatory bowel disease, diverticulitis, cholecystitis, symptomatic cholangitis or appendicitis, acute pancreatitis, acute obstruction of the pancreatic duct or common bile duct, or gastric outlet obstruction

• Inability to swallow tablets

• Uncontrollable ascites or pleural effusion

• Cavitating pulmonary lesion(s) or known endotracheal or endobronchial disease manifestation

• Clinically significant hematuria, hematemesis, or hemoptysis, or other history of significant bleeding within 12 weeks

• Lesions invading any major blood vessels

• Receipt of the last dose of anticancer therapy less than 28 days prior to the first dose of study drug

• Major surgery within 8 weeks before first dose of study treatment

• History of allogenic organ transplantation

• Active infection including tuberculosis, hepatitis B, hepatitis C, or human immunodeficiency virus. Patients with a past or resolved hepatitis B virus (HBV) infection are eligible. Patients positive for hepatitis C antibody are eligible only if polymerase chain reaction is negative for hepatitis C virus (HCV) RNA

• Receipt of live attenuated vaccine within 30 days prior to the first dose of study drug

• Uncontrolled intercurrent illness, including but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, interstitial lung disease, or serious chronic gastrointestinal conditions

• Uncontrolled hypertension defined as sustained blood pressure (BP) > 150 mm Hg systolic or > 100 mm Hg diastolic despite optimal antihypertensive treatment

• Prolonged baseline QT interval corrected for heart rate greater than 470 ms

• Brain metastases or spinal cord compression. Patients whose brain metastases have been treated may participate provided they show radiographic stability

• Known allergy or hypersensitivity to any of the study drugs or any of the study drug excipients

• Current or anticipated use of other investigational agents while participating in this study

• History of another primary malignancy except for:

  • Malignancy treated with curative intent and with no known active disease before the first dose of investigational product (IP) and of low potential risk for recurrence
  • Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease
  • Adequately treated carcinoma in situ without evidence of disease

• Psychiatric illness/social situations that would limit compliance with study requirements

• Pregnant or breast feeding