TReatment of ADC-Refractory Breast CancEr With Dato-DXd or T-DXd: TRADE DXd

This is a multi-institutional, open-label, phase 2 trial assessing the efficacy of sequential antibody drug conjugate (ADC) treatment with Dato-DXd or T-DXd in patients with HER2-negative (HER2-low and HER2-0) locally advanced unresectable or metastatic breast cancer (MBC). There are two parts to this study, which has a sequential design. Most participants will enroll in Group 1, which has two different study drugs. A participant will be randomized to receive one of the two study drugs, and if there is progression of disease on the study drug that was originally assigned, a participant will crossover to a different arm in Group 2 and receive the other study drug. Some participants may enroll directly to Group 2 if they already received the first drug. The goal is to evaluate the effectiveness of sequential ADC therapy by switching the target of the ADC. Randomization means participants are placed into a treatment arm by chance. Participants will be randomized into one of four treatment arms in Group 1: * Arm A: Trastuzumab deruxtecan in hormone receptor (HR)-positive metastatic breast cancer (MBC) * Arm B: Trastuzumab deruxtecan in HR-negative MBC * Arm C: Datopotamab deruxtecan in HR-positive MBC * Arm D: Datopotamab deruxtecan in HR-negative MBC Participants may crossover to one of the below treatment arms in Group 2: * Arm E: Datopotamab deruxtecan in HR-positive MBC * Arm F: Datopotamab deruxtecan in HR-negative MBC * Arm G: Trastuzumab deruxtecan in HR-positive MBC * Arm H: Trastuzumab deruxtecan in HR-negative MBC The U.S. Food and Drug Administration (FDA) has not approved Datopotamab deruxtecan as a treatment for HER2-low metastatic breast cancer. The U.S. FDA has approved Trastuzumab deruxtecan for previously treated HER2-low metastatic breast cancer, and for other uses. The research study procedures include screening for eligibility, study treatment visits, blood tests, tumor biopsies, questionnaires, echocardiograms, electrocardiograms, Computerized Tomography (CT) scans, Magnetic Resonance Imaging (MRI) scans, and eye exams. Participants will receive study treatment for as long as there is benefit. After the study treatment ends, participants will be followed approximately every six months thereafter. It is expected that about 357 people will take part in this research study. AstraZeneca is supporting this research study by providing the study drugs and funding.