Phase Ib Study of the Safety of T-DXd and Immunotherapy Agents With and Without Chemotherapy in Advanced or Metastatic HER2+, Non-squamous NSCLC

Inclusion criteria: * Histologically documented unresectable locally advanced/metastatic non-squamous NSCLC * Part 1: Progression after 1 or 2 lines of systemic therapy for recurrent or metastatic setting. * Part 3, Part 4 and Part 5: Patients must have tumors that do not harbor known genomic alterations or actionable driver kinases, for which approved therapies are available are allowed. * Part 3, Part 4 and Part 5: Patient must be treatment-naïve for advanced or metastatic NSCLC. Patients who have received prior adjuvant, or neoadjuvant chemotherapy, or definitive chemoradiation for advanced disease are eligible, provided that progression has occurred \> 6 months from end of last therapy * HER2overexpression status as determined by central review of tumor tissue * WHO / ECOG performance status of 0 or 1 * Measurable target disease assessed by the investigator using RECIST 1.1 * Has protocol defined adequate organ and bone marrow function * Part 3, Part 4 and Part 5: Minimum body weight of 35 kg. Exclusion criteria: * HER2 mutation if previously known * Has a history of (non-infectious) ILD/pneumonitis that required steroids, has current ILD/pneumonitis, or where suspected ILD/pneumonitis cannot be ruled out by imaging at screening * Lung-specific intercurrent clinically significant illnesses including, but not limited to, any underlying pulmonary disorder and prior pneumonectomy * Active primary immunodeficiency known HIV infection, or active chronic and resolved hepatitis B (positive hepatitis B virus surface antigen \[HBsAg+ve\] or hepatitis B virus core antibody (anti-HBc +ve) regardless of HBV DNA level)) or hepatitis C infection. Patients positive for HCV antibody are eligible only if polymerase chain reaction is negative for HCV RNA. Patients should be tested for HIV prior to treatment assignment if required by local regulations or IRB/EC * Active infection including tuberculosis and uncontrolled infection requiring IV antibiotics, antivirals, or antifungals * Spinal cord compression or clinically active central nervous system metastases, defined as untreated and symptomatic, or requiring therapy with corticosteroids or anticonvulsants to control associated symptoms * Medical history of myocardial infarction within 6 months before treatment assignment, symptomatic CHF (New York Heart Association Class II to IV), clinically important cardiac arrhythmias, or a recent (\< 6 months) cardiovascular event including stroke * For Part 3, Part 4 and Part 5: Cardiomyopathy of any etiology, symptomatic CHF (as defined by New York Heart Association Class \> II), unstable angina pectoris, history of MI within the past 12 months, or cardiac arrhythmia are to be excluded. Patients with troponin levels above ULN at screening (as defined by the manufacturer), and without any myocardial related symptoms, should have a cardiologic consultation before treatment assignment to rule out acute cardiopulmonary events. * Ascites or pericardial effusion that requires drainage, peritoneal shunt, Pleuroperitoneal shunt or CART (Concentrated Ascites Reinfusion Therapy) * For Part 3, Part 4 and Part 5: Active non-infectious skin disease (including any grade rash, urticarial, dermatitis, ulceration, or psoriasis) requiring systemic treatment, active or prior documented autoimmune or inflammatory disorders requiring chronic treatment with steroids or other immunosuppressive treatment. * Unresolved toxicities not yet resolved to Grade ≤ 1 or baseline from previous anticancer therapy OR prior discontinuation of any planned study therapy due to toxicity. * must not have any medical contraindication to platinum-based chemotherapy. * Part 3, Part 4 and Part 5 patients must not have had prior exposure to anti-PD-1, anti-PD-L1, anti-CTLA-4, anti-TIGIT or any other experimental immunotherapy in any setting. * For Part 3, Part 4 and Part 5: History of substance abuse or any other medical or psychological conditions that may, in the opinion of the Investigator, interfere with the subject's participation in the clinical study or evaluation of the clinical study results * For Part 3, Part 4 and Part 5: History of thromboembolic events within 3 months before the first dose of IP (limited to pulmonary embolism, deep vein thrombosis, or cerebral venous sinus thrombosis).