Participants will receive study treatment with agenT-797, botensilimab, balstilimab, ramucirumab, and paclitaxel. When participants start each agent will depend on how their disease is affecting them.

Inclusion Criteria:

• Metastatic or advanced unresectable adenocarcinoma of esophageal, gastric, or gastroesophageal junction
• Disease progression on one prior line of therapy for metastatic disease. Patients with previously untreated advanced unresectable or metastatic disease may be included if disease progressed or recurred during neoadjuvant or adjuvant therapy or within 6 months of completion of those treatments.
• Patients must have histologically or cytologically confirmed esophageal, gastric, or gastroesophageal junction adenocarcinoma
• Patients must have measurable or evaluable disease as defined by RECIST v1.1 criteria. Patients with evaluable disease must be eligible to begin with an induction cycle
• Age 18 years or older
• ECOG performance status 0 to 1
• Adequate organ function as defined in Table 2

Table 2. Organ function requirements for eligibility Hematological Absolute neutrophil count: ≥1000/mcL Platelets: ≥90,000/mcL Hemoglobin: ≥8 g/dL Renal Serum creatinine: ≤1.5X ULN Hepatic Serum total bilirubin: ≤1.5X ULN OR Direct bilirubin ≤ULN for subjects with total bilirubin levels >1.5X ULN, except patients with Gilbert's disease (≤3X ULN) AST and ALT: ≤2.5X ULN Albumin: ≥3 mg/dL

Exclusion Criteria:

• Received prior therapy with ramucirumab at any time
• Received paclitaxel or docetaxel-based therapy within 6 month of study enrollment
• Had a prior grade >3 immune related adverse event due to anti-PD-1, anti-PD-L1, anti-PD-L2, or anti-CTLA4 therapy at any time
• Diagnosis of immunodeficiency or receipt of systemic steroid therapy or any other form of immunosuppressive therapy within 7 days before the first dose of trial treatment. Replacement therapy (ie physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic immunosuppressive therapy and is allowed.
• History of gastrointestinal perforation or fistulae
• A known history of active Bacillus tuberculosis
• Known active central nervous system metastases and/or carcinomatous meningitis
• History of or any evidence of active, non-infectious, immune-mediated pneumonitis. Patients with radiation-induced pneumonitis who are asymptomatic are permitted on study.
• Peripheral neuropathy limiting ADLs
• A known history of human immunodeficiency virus (HIV 1/2 antibodies)
• Known active hepatitis B (e.g., HBsAg reactive) or hepatitis C (e.g., HCV RNA [qualitative] is detected). Patients with HBsAg reactive on entecavir may be eligible after consultation with hepatologist and study team.
• Received a live vaccine within 30 days of planned start of study therapy
• Known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial
• Pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the trial, starting with the prescreening or screening visit through 5 months after the last dose of trial treatment
• Unwilling to give written, informed consent, unwilling to participate, or unable to comply with the protocol for the duration of the study

Memorial Sloan Kettering Cancer Center supports the international committee of medical journal editors (ICMJE) and the ethical obligation of responsible sharing of data from clinical trials. The protocol summary, a statistical summary, and informed consent form will be made available on clinicaltrials.gov when required as a condition of Federal awards, other agreements supporting the research and/or as otherwise required. Requests for deidentified individual participant data can be made beginning 12 months after publication and for up to 36 months post publication. Deidentified individual participant data reported in the manuscript will be shared under the terms of a Data Use Agreement and may only be used for approved proposals. Requests may be made to: crdatashare@mskcc.org.