Cinrebafusp Alfa in Combination With Ramucirumab and Paclitaxel in HER2-High Gastric or GEJ Adenocarcinoma and in Combination With Tucatinib in HER2-Low Gastric or GEJ Andenocarinoma

Inclusion Criteria: 1. Signed written informed consent obtained prior to performing any study procedure, including screening procedures 2. Men and women ≥18 years of age 3. Eastern Cooperative Oncology Group (ECOG) Performance Status 0 or 1 4. Histologically or cytologically confirmed gastric or GEJ adenocarcinoma 5. Arm 1: Has received no more than two prior treatment regimens for advanced disease, including a platinum, a fluoropyrimidine, and HER2-directed therapy such as trastuzumab Arm 2: Has received at least one prior treatment regimen for advanced disease 6. Arm 1: Demonstration of HER2 positivity assessed by a test with appropriate regulatory validation in a current tissue specimen and following guidelines for assessment in gastric or GEJ adenocarcinoma described in Section 4.3 after receiving no more than two prior treatment regimens, including a platinum, a fluoropyrimidine, and HER2-directed therapy such as trastuzumab Arm 2: Demonstration of HER2 IHC 1+ or IHC 2+ without HER2/neu amplification assessed by a test with appropriate regulatory validation in a current tissue specimen and following guidelines for assessment in gastric or GEJ adenocarcinoma described in Section 4.3 after completion of the most recent prior treatment regimen 7. Measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 8. Adequate organ and hematologic function as defined below: * Serum AST and ALT ≤2.5 × upper limit of normal (ULN) or ≤5 × ULN in the presence of liver metastases * Total serum bilirubin ≤1.5 × ULN * Serum albumin ≥ 3g/dL * Serum creatinine ≤1.5 × ULN OR creatinine clearance measured via 24-hour urine collection ≥40 mL/min if serum creatinine is \> 1.5X ULN * Arm 1 only: Urinary protein is ≤ 1+ on dipstick or routine urine analysis; if urine dipstick or urinalysis is ≥ 2+, a 24-hour urine collection for protein must demonstrate \< 1000 mg of protein in 24 hours * Hemoglobin ≥ 9 g/dL; packed red blood cell transfusions are not allowed in the week preceding screening evaluation * ANC ≥ 1500/mm3 * Platelet count ≥ 100,000/mm3 * INR ≤1.5 and PT ≤1.5 × ULN and PTT ≤1.5 × ULN. Arm 1 only: Patients receiving oral anti-coagulants must be switched to low molecular weight anti-coagulants and have achieved stable coagulation profile prior to first dose of protocol therapy. Arm 2 only: Patients receiving oral anti-coagulants must be switched to low molecular weight heparin and have achieved stable coagulation profile prior to first dose of protocol therapy. 9. Left ventricular ejection fraction (LVEF) of ≥ 50% as determined by echocardiogram or multigated acquisition scan 10. Resolution to Grade ≤1 by NCI CTCAE v5.0 of all clinically significant toxicities associated with prior therapy or procedures 11. If sexually active, the patient must be post-menopausal, surgically sterile or using highly effective contraception. Highly effective contraception for women of child-bearing potential and males with female partners of child-bearing potential is defined as 1 barrier method (e.g., condom) and 1 additional method (e.g., hormonal) of contraception during the study and for at least three months from the last study treatment or recommended contraceptive period according to the local label of the concomitant drug if greater than 3 months 12. Women of child-bearing potential may not be breastfeeding and must have a negative serum pregnancy test within 96 hours prior to start of study treatment Exclusion Criteria: 1. Disease of squamous or undifferentiated histology 2. History or evidence of known active CNS metastases or carcinomatous meningitis. Patients with brain metastases are eligible provided they have shown clinical and radiographic stable disease for at least 4 weeks after definitive therapy and have not used steroids (\> 10 mg/day of prednisone or equivalent) for at least 2 weeks prior to the first dose of study treatment 3. Arm 1 only: Receipt of any previous systemic therapy (including investigational agents) targeting the VEGF or the VEGFR signaling pathways 4. Intolerance to trastuzumab or other HER2-directed agent in prior treatment regimen 5. History of deep vein thrombosis (DVT), pulmonary embolism (PE) or any other significant thromboembolism during the three months prior to first dose of study treatment; venous port or catheter thrombosis or superficial venous thrombosis are not considered significant (Arm 1 only). For patients in Arm 2, the investigator is referred to Exclusion Criterion 21 and should consult with the Medical Monitor in the case of a history of these or similar events. 6. Chronic therapy with nonsteroidal anti-inflammatory drugs (NSAIDs; e.g., indomethacin, ibuprofen, naproxen or similar agents) or other antiplatelet agents (e.g., clopidogrel, ticlopidine, dipyridamole, anagrelide); aspirin up to 325 mg per day is permitted 7. Significant bleeding disorders, vasculitis or a significant bleeding episode from the GI tract within 3 months prior to study entry 8. Arterial thromboembolic event within 6 months prior to study entry 9. History of acute coronary syndromes, including myocardial infarction, coronary artery bypass graft, unstable angina, coronary angioplasty or stenting within past 24 weeks 10. History of or current Class II, III or IV heart failure as defined by the New York Heart Association (NYHA) functional classification system or symptomatic or poorly controlled cardiac arrhythmia 11. History of ejection fraction drop below the lower limit of normal with trastuzumab or other HER2-directed therapy 12. Uncontrolled or poorly-controlled hypertension (arterial hypertension ≥150 mm Hg or diastolic ≥90 mmHg) for \> four weeks despite standard medical management; the patient may be re-screening after treatment for hypertension 13. Any arterial thromboembolic event, including but not limited to myocardial infarction, transient ischemic attack, cerebrovascular accident or unstable angina, within six months prior to first dose of study treatment 14. Bowel obstruction, history or presence of inflammatory enteropathy or extensive intestinal resection (hemicolectomy or extensive small intestine resection with chronic diarrhea), Crohn's disease, ulcerative colitis or chronic diarrhea 15. Gastrointestinal perforation or fistula within 6 months prior to study entry or have risk factors for perforation (these events may be acceptable for patients enrolled in Arm 2 after discussion with the Medical Monitor) 16. Grade 3 or Grade 4 GI bleeding within 3 months prior to first study treatment (these events may be acceptable for patients enrolled in Arm 2 after discussion with the Medical Monitor) 17. Arm 2 only: Inability to swallow pills or presence of any significant gastrointestinal disease which would preclude the adequate absorption of an oral medication. 18. Cirrhosis at a level of Child-Pugh B or worse OR cirrhosis of any degree and a history of hepatic encephalopathy or hepatorenal syndrome or clinically meaningful ascites resulting from cirrhosis. Clinically meaningful cirrhosis is defined as ascites from cirrhosis requiring diuretics or paracentesis. 19. Serious or non-healing wound, ulcer or bone fracture within 28 days prior to first study treatment (these events may be acceptable for patients enrolled in Arm 2 after discussion with the Medical Monitor) 20. Any medical, psychiatric, cognitive or other condition that compromises the patient's ability to understand information, to give informed consent or to comply with the study protocol 21. Any severe concurrent disease or condition (including active infection, cardiac arrhythmia, interstitial lung disease) that in the judgment of the Investigator would make study participation inappropriate for the patient 22. Arm 2 only: Prior anthracycline exposure (epirubicin \> 720 mg/m2) 23. Arm 2 only: Having used a strong cytochrome P450 CYP2C8 inhibitor within three elimination half-lives of the inhibitor or have used a strong CYP3A4 or moderate/strong CYP2C8 inducer within five days prior to first dose of study treatment. Patients on the strong CYP2C8 inhibitor gemfibrozil at screening must discontinue its use at least 24 hours before the first dose of study drug and if needed, substitute an alternate lipid-lowering agent. 24. Active human immunodeficiency virus (HIV) disease, hepatitis B, or hepatitis C 25. Any severe infection within 28 days prior to study start or requirement for oral or intravenous antibiotics within 14 days prior to study start 26. Administration of live attenuated vaccines within 28 days prior to start of treatment or anticipated need for vaccination with live attenuated vaccine during the study. Vaccination for SARS-CoV-2 is permitted: * Patients in screening, who have not started study treatment, and who are receiving a two-dose vaccine should schedule their vaccination(s) to receive the second dose at least two weeks prior to initiation of treatment (Cycle 1, Day 1). * If the patient is receiving a single-dose vaccine, the single dose should be at least two weeks prior to initiation of treatment (Cycle 1, Day 1). * Vaccination during Cycle 1 between the first and the second cycle of cinrebafusp alfa is discouraged. * Beginning with Cycle 2 a minimum of 7 days must elapse from last study treatment to administration of vaccine and patients must have seven days elapse from vaccination to next treatment on study. * Efforts should be made to avoid treatment delays, but where necessary a delay of up to seven days in next treatment of the study drug will be permitted. 27. History of infusion or other reactions to any components/excipients of cinrebafusp alfa (Arm 1 and Arm 2), or ramucirumab or paclitaxel (Arm 1); Arm 2 only: history of allergic reactions to tucatinib or compounds chemically or biologically similar to tucatinib, or known allergy to any of the excipients in tucatinib 28. History of severe hypersensitivity reactions to monoclonal antibodies or Grade ≥3 immune-mediated adverse reaction to immune checkpoint inhibitor agents 29. Systemic steroid therapy (\>10 mg daily prednisone or equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study treatment; topical, inhaled, nasal and ophthalmic steroids are not prohibited 30. History of autoimmune disease that has required systemic treatment with disease-modifying agents, corticosteroids, or immunosuppressive drugs unless in the opinion of the investigator the patient is in a complete and durable remission; physiologic replacement therapies, such as thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, is allowed 31. Prior organ transplantation including allogeneic or autologous stem cell transplantation 32. Arm 2 only: Prior receipt of HER2-directed and/or EGFR-directed tyrosine kinase inhibitor (TKI) agents 33. Concurrent or previous other malignancy within 3 years of study entry with the exception of cured basal or squamous cell skin cancer, superficial bladder cancer, prostate intra-epithelial neoplasm, carcinoma in situ of the cervix, or other non-invasive or indolent malignancy 34. Receipt of an investigational agent, chemotherapy or other cancer-directed therapy within 4 weeks (6 weeks for nitrosoureas and mitomycin C) of initiation of study treatment 35. Receipt of radiation therapy within 4 weeks of scheduled Day 1 dosing, unless the radiation comprised a limited field to non-visceral structures; palliative radiotherapy is permitted 36. Receipt of trastuzumab or adotrastuzumab emtansine or any other commercial or experimental drug that engages the same epitope as trastuzumab within 4 weeks of scheduled C1D1 dosing 37. Concurrent enrollment in another therapeutic clinical study 38. Major surgery within 28 days of scheduled C1D1 dosing or minor surgery or subcutaneous venous access device placement within 7 days prior to initiation of study treatment or elective or planned major surgery to be performed during the course of the clinical trial (these events may be acceptable for patients enrolled in Arm 2 after discussion with the Medical Monitor)