Paclitaxel and Ramucirumab +/- Zanidatamab in HER2 Postive Advanced Gastroesophageal Adenocarcinoma

Inclusion Criteria: * Participants must have histologically or pathologically confirmed gastroesophageal adenocarcinoma (stomach, gastroesophageal junction or esophagus) that is unresectable or metastatic and which must be HER2 positive as confirmed by central testing using FDA-approved HER2 assay. HER2 positive is defined as IHC 3+, or IHC 2+ and FISH positive. * Participants must have received and failed at least one prior trastuzumab-containing regimen in combination with platinum-based chemotherapy for treatment of locally advanced or metastatic disease. Failure is defined as demonstrated objective disease progression (radiologic) on the most recently administered HER2 targeting agent. * Participants must have presence of measurable or evaluable disease as defined by Response Evaluation Criteria in Solid Tumours (RECIST 1.1). * Participants must be considered a suitable candidate for, and able to receive chemotherapy for advanced disease with paclitaxel and ramucirumab. * Participants must consent to the provision of samples of blood, serum and plasma in order that the specific correlative marker assays may be conducted. * Participants must consent to provision of, and investigator(s) must confirm access to a representative formalin fixed paraffin embedded (FFPE) block of tumour tissue/ or a predetermined number of freshly cut slides of representative tumour tissue of adequate amount and quality in order that the central HER2 testing may be done * Participants must be ≥ 18 years of age. * Participants must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Participants must have a life expectancy of at least 12 weeks at the time of study entry * Imaging investigations including CT/MRI of chest/abdomen/pelvis or other scans as necessary to document all sites of disease must be done within 28 days prior to randomization * Participants must have adequate cardiac function by ECHO or MUGA defined as EF ≥ 50%. This is to be performed within 4 weeks (preferred) but no more than 8 weeks prior to randomization * Participants must have adequate normal organ and marrow function * Participant is able (i.e. sufficiently fluent) and willing to complete the quality of life and/or health utility questionnaires in either English or French * Participant consent must be appropriately obtained in accordance with applicable local and regulatory requirements. * Participant must be accessible for treatment and follow-up. Investigators must assure themselves the participants enrolled on this trial will be available for complete documentation of the treatment, adverse events, and follow-up. * In accordance with CCTG policy, protocol treatment is to begin within 2 working days of participant enrollment * Participants of childbearing potential must have agreed to use a highly effective contraceptive method for the entire period of study treatment and for at least 7 months after discontinuing study therapy. Exclusion Criteria: * Participants with a history of other malignancies except: adequately treated non-melanoma skin cancer, curatively treated in-situ cancer of the cervix, or other solid tumours curatively treated with no evidence of disease for ≥ 5 years. Patients with a history of other malignancies detected at an early stage and whom the investigator believes have been curatively treated and are at a low risk of recurrence MAY be eligible * Participants receiving therapy in a concurrent clinical study. Patients must agree not to participate in other clinical studies during their participation in this trial while on study treatment * Participants with active or uncontrolled intercurrent illness * Participants with human immunodeficiency virus infection (positive HIV 1/2 antibodies), active hepatitis B infection (positive HBV surface antigen (HBsAg)) or positive for hepatitis C (HCV) antibody may be considered for enrollment, if infection is adequately controlled in the opinion of the investigator. * Any active disease condition which would render the protocol treatment dangerous or impair the ability of the patient to receive protocol therapy * Any condition (e.g. psychological, geographical, etc.) that does not permit compliance with the protocol * Any unresolved toxicity (CTCAE grade 2 or greater) from previous anti-cancer therapy which in the opinion of the investigator puts the participant at higher than expected risk during protocol treatment. However, participants with irreversible toxicity that is not reasonably expected to be exacerbated by the investigational products in the Investigator's opinion may be included.