A Study of Ivonescimab in Combination With Dato-DXd or Osimertinib in People With Non-Small Cell Lung Cancer

Inclusion Criteria: * Written informed consent by participant * Biopsy-proven metastatic non-small cell lung cancer * Somatic activating mutation in EGFR in pre-treatment tumor biopsy or cfDNA (including all mutations with sensitivity to osimertinib) by any CLIA certified assay. * Prior treatment with 3rd-generation EGFR TKI therapy and platinum-based chemotherapy (or ineligible for platinum-based chemotherapy) * At least one measurable (RECIST 1.1) indicator lesion not previously irradiated * ECOG PS 0-1 * Age ≥18 years old * Ability to swallow oral medications (Study Cohort B only) * Adequate organ function * AST, ALT ≤ 2.5 x ULN; For patients with liver metastases, AST and ALT ≤ 5 × ULN * Total bilirubin ≤ 1.5x ULN; For patients with liver metastases or confirmed/suspected Gilbert syndrome, TBIL ≤3 × ULN Creatinine clearance (CrCl) ≥ 50 mL/min using the Cockcroft-Gault formula or estimated glomerular filtration rate (eGFR) value ≥50 mL/min using the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation * Urine protein \< 2+ or 24 hour urine protein quantification \< 1.0 g * Absolute neutrophil count (ANC) ≥ 1500 cells/mm\^3 * Hemoglobin ≥ 9.0 g/dL (red blood cell/plasma transfusion is not allowed within 2 weeks prior to screening assessment) * Platelets ≥100,000/mm3 (platelet transfusion is not allowed within 10 days prior to screening assessment) * Coagulation: prothrombin time (PT) or international normalized ratio (INR) ≤ 1.5 × ULN, and partial prothrombin time (PTT) or activated partial thromboplastin time (aPTT) ≤ 1.5 × ULN (unless abnormalities are unrelated to coagulopathy). This applies only to patients who are not on therapeutic anti-coagulation. Patients receiving therapeutic anti-coagulation should be on a stable dose. * Female patients of childbearing age must have negative serum pregnancy test and a negative urine pregnancy test on the day of first dose prior to dosing. * Female patient of childbearing potential having sex with an unsterilized male partner must agree to use a highly effective method of contraception from the beginning of screening until 90 days after the last dose of the ivonescimab and/or 3 months after last dose of Dato-DXd or 6 weeks after last dose of osimertinib * Unsterilized male patients having sex with a female partner of childbearing potential, or a pregnant or breastfeeding partner must agree to use barrier contraception (male condom plus spermicide) for the duration of the treatment period until 90 days after the last dose of ivonescimab and/or 6 months after the last dose of Dato-DXd or 6 weeks after last dose osimertinib. Male patients with female partners of childbearing potential must have the female partner agree to use at least 1 form of highly effective contraception for the duration of the treatment period until 90 days after the last dose of ivonescimab and/or 3 months after the last dose of Dato-DXd or 6 weeks after last does of osimertinib. Exclusion Criteria: * EGFR exon 20 insertion positive lung cancer with expected lack of sensitivity to osimertinib (Study Cohort B only). * Pregnant or lactating women * Participation in another clinical study and receiving treatment with an investigation product during the last 4 weeks before enrollment * Prior exposure to anti-PD-1 inhibitor therapy * Prior exposure to antibody drug conjugate (ADC) containing chemotherapeutic agent targeting topoisomerase I, TROP2 antibody (Study Cohort A only). * History of clinically significant corneal disease (Study Cohort A only) * Poorly controlled hypertension with repeated systolic blood pressure ≥ 150 mmHg or diastolic blood pressure ≥ 100 mmHg after oral antihypertensive therapy * Major surgical procedures or serious trauma within 4 weeks of study enrollment, or plans for major surgical procedures within 4 weeks after the first dose (as determined by the investigator). Minor local procedures (excluding central venous catheterization and port implantation) within 3 days prior study enrollment. * History of bleeding tendencies or coagulopathy and/or clinically significant bleeding symptoms or risk within 4 weeks of study enrollment, including but not limited to: * Hemoptysis (defined as coughing up ≥ 0.5 teaspoon of fresh blood or small blood clots). Note: transient hemoptysis associated with diagnostic bronchoscopy is allowed. * Significant nasal bleeding /epistaxis (bloody nasal discharge is allowed) * Current use of prophylactic or full-dose anticoagulants or anti-platelet agents for therapeutic purposes that is not stable prior to first study drug treatment is not allowed. The use of full-dose anticoagulants is permitted as long as the international normalized ratio (INR) or activated partial thromboplastin time (aPTT) is within therapeutic limits according to the medical standard of the enrolling institution. * Active (eg, with disease modifying drugs, prednisone \>10 mg daily or equivalent, immunosuppressant therapy) or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., colitis or Crohn's disease\], diverticulitis \[with the exception of diverticulosis\], systemic lupus erythematosus, Sarcoidosis syndrome, or Wegener syndrome \[granulomatosis with polyangiitis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc\]). The following are exceptions to this criterion: * Short course of steroids if given for infection * Replacement therapy (eg, thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is permitted. * Intermittent use of bronchodilators, inhaled corticosteroids, or local corticosteroid injections is permitted * Patients with vitiligo or alopecia * Patients with hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement * Any chronic skin condition that does not require systemic therapy * Patients without active disease in the last 5 years may be included but only after consultation with the study physician * Patients with celiac disease controlled by diet alone * History of major diseases before first study drug treatment, specifically: * Unstable angina, myocardial infarction, congestive heart failure (New York Heart Association \[NYHA\] classification ≥ grade 2) or unstable vascular disease (eg, aortic aneurysm at risk of rupture, Moyamoya disease) that required hospitalization within 12 months prior to first study drug treatment, or other cardiac impairment that may affect the safety evaluation of the study drug (eg, poorly controlled arrhythmias, myocardial ischemia) * History of esophageal gastric varices, severe ulcers, wounds that do not heal, abdominal fistula, intra-abdominal abscesses, or acute gastrointestinal bleeding within 6 months of study enrollment * History of any grade arterial thromboembolic event as specified in National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) 5.0, transient ischemic attack, cerebrovascular accident, hypertensive crisis, or hypertensive encephalopathy within 12 months before first ivonescimab infusion * Acute exacerbation of chronic obstructive pulmonary disease within 4 weeks before first ivonescimab infusion * History of perforation of the gastrointestinal tract and/or fistula, history of gastrointestinal obstruction (including incomplete intestinal obstruction requiring parenteral nutrition), extensive bowel resection (partial colectomy or extensive small bowel resection) within 6 months before first ivonescimab infusion * Imaging during the screening period shows that the patient has: * Radiologically documented evidence of major blood vessel invasion (central pulmonary artery, central pulmonary veins, aorta, brachiocephalic artery, common carotid artery, subclavian artery, superior vena cava) or tumor invading organs (heart, trachea, esophagus, central bronchi \[not including segmental bronchi\]) or if there is a risk of esophagotracheal or esophagopleural fistula in the opinion of the investigator. * Radiographic evidence of major blood vessel encasement with narrowing of the vessel or intratumor lung cavitation or necrosis that the investigator determines will pose a significantly increased risk of bleeding. * History of another primary malignancy except for: * Malignancy treated with curative intent and with no known active disease ≥ 2 years before the first dose of study drugs 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 * Symptomatic CNS metastases, CNS metastases with hemorrhagic features, CNS radiation within 7 days prior to first study drug treatment, potential need for CNS radiation within the first cycle, or symptomatic leptomeningeal disease. Note: Patients must have stopped corticosteroids or be on physiologic corticosteroid replacement therapy (prednisone ≤ 10 mg daily or equivalent). * Live vaccine or live attenuated vaccine within 4 weeks prior to first ivonescimab infusion, or if scheduled to receive a live vaccine or live attenuated vaccine during the study period. Inactivated vaccines are permitted. * Severe infection within 4 weeks prior to first ivonescimab infusion, including but not limited to comorbidities requiring hospitalization, sepsis, or severe pneumonia; active infection (as determined by the investigator) requiring systemic anti-infective therapy within 2 weeks prior to first study drug treatment (excluding antiviral therapy for hepatitis B or C) * Has pre-existing peripheral neuropathy that is ≥ Grade 2 by CTCAE version 5 * Uncontrolled pleural effusions, pericardial effusions, or ascites that is clinically symptomatic Note: Patients managed with indwelling catheters (eg, PleurX) are allowed. * History of interstitial lung disease (ILD) requiring steroids * Current use of systemic corticosteroids (\>10 mg daily prednisone or equivalent) * Known history of human immunodeficiency virus (HIV) whose viral load is not controlled. * Known history of allogeneic organ transplantation or allogeneic hematopoietic stem cell transplantation * Patients with active hepatitis B are required to have stable or declining levels of hepatitis B DNA by polymerase chain reaction (PCR) on appropriate anti-viral therapy with acceptable tolerability for one month prior to first study drug treatment. All patients with active hepatitis C (hepatitis C virus \[HCV\] antibody positive with HCV RNA levels above the lower limit of detection) are excluded. * Known allergy to any component of any study drug; known history of severe hypersensitivity to other monoclonal antibodies * History or current evidence of any condition (medical \[including adverse events from prior anticancer therapy, disorders secondary to tumor\], surgical or psychiatric \[including substance abuse\]), or laboratory abnormality that might confound the results of the study, interfere with the patient's participation for the full duration of the study, might lead to higher medical risk and/or is not in the best interest of the patient to participate, in the opinion of the treating investigator.