A Study of T-DXd in Participants With or Without Brain Metastasis Who Have Previously Treated Advanced or Metastatic HER2 Positive Breast Cancer

Inclusion: * Participants should have pathologically documented breast cancer that is: unresectable/advanced or metastatic; confirmed HER2-positive status expression as determined according to American Society of Clinical Oncology/College of American Pathologists guidelines * Participant must have either: no evidence of BM, or untreated BM on screening contrast brain magnetic resonance imaging/ computed tomography (MRI/CT) scan, not needing immediate local therapy or previously-treated stable or progressing BM * Participants with BMs must be neurologically stable * For participants requiring radiotherapy due to BMs, there should be an adequate washout period before day of first dosing: * ≥ 7 days since stereotactic radiosurgery or gamma knife * ≥ 21 days since whole brain radiotherapy * Eastern Cooperative Oncology Group performance status 0-1 * Previous breast cancer treatment: radiologic or objective evidence of disease progression on or after HER2 targeted therapies and no more than 2 lines/regimens of therapy in the metastatic setting * Participant with the following measurable: at least 1 lesion that can be accurately measured at baseline as ≥ 10 mm in the longest diameter with CT or MRI and is suitable for accurate repeated measurements; or following Non-measurable diseases: Non-measurable, bone-only disease that can be assessed by CT or MRI or X-Ray. Lytic or mixed lytic bone lesions that can be assessed by CT or MRI or X-ray in the absence of measurable disease as defined above is acceptable; Participants with sclerotic/osteoblastic bone lesions only in the absence of measurable disease are not eligible; and Non-measurable CNS disease (Cohort 2 only) * Adequate organ and bone marrow function within 14 days before the day of first dosing as defined in the protocol * Left ventricular ejection fraction ≥ 50% within 28 days before enrollment * Negative pregnancy test (serum) for women of childbearing potential Exclusion Criteria * Known or suspected leptomeningeal disease * Prior exposure to tucatinib treatment * Refractory nausea and vomiting, chronic gastrointestinal disease, or previous significant bowel resection that would preclude adequate absorption, distribution, metabolism, or excretion of T-DXd * History of another primary malignancy except for malignancy treated with curative intent with no known active disease within 3 years before the first dose of study intervention and of low potential risk for recurrence * Based on screening contrast brain MRI/CT scan, participants must not have any of the following: any untreated brain lesions \> 2.0 cm in size; ongoing use of systemic corticosteroids for control of symptoms of BMs; any brain lesion thought to require immediate local therapy; have poorly controlled (\> 1/week) generalized or complex partial seizures, or manifest neurologic progression due to BMs not withstanding CNS-directed therapy * Has spinal cord compression * Known active hepatitis B or C infection, such as those with serologic evidence of viral infection within 28 days of Cycle 1 Day 1. Participants with past or resolved hepatitis B virus infection are eligible, if negative for hepatitis B surface antigen and positive for anti-hepatitis B core antigen * Participants positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV RNA * Uncontrolled infection requiring IV antibiotics, antivirals, or antifungals * Receipt of live, attenuated vaccine within 30 days prior to the first dose of T-DXd * Participants with a medical history of myocardial infarction within 6 months before screening, symptomatic congestive heart failure (New York Heart Association Class II to IV) * 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 and any autoimmune, connective tissue or inflammatory disorders * Prior exposure, without adequate treatment washout period before the day of first dosing, to chloroquine/hydroxychloroquine: \< 14 days * Anticancer chemotherapy: immunotherapy (non-antibody-based therapy), retinoid therapy, hormonal therapy: \< 3 weeks * \< 6 weeks for nitrosoureas or mitomycin * Antibody-based anticancer therapy: \< 4 weeks * Any concurrent anticancer treatment. Concurrent use of hormonal therapy for noncancer- related conditions is allowed * Unresolved toxicities from previous anticancer therapy, defined as toxicities (other than alopecia) not yet resolved to Grade ≤ 1 or baseline * Palliative radiotherapy with a limited field of radiation within 2 weeks or with wide field of radiation, radiation to the chest, or to more than 30% of the bone marrow within 4 weeks before the first dose of study intervention * Participants with prior exposure to immunosuppressive medication within 14 days prior to first study dose * Participants with a known hypersensitivity to study intervention or any of the excipients of the product or other monoclonal antibodies