Inclusion Criteria  Age  Participant must be ≥ 18 years (≥ 20 years in Japan) at the time of screening.  Type of Participant and Disease Characteristics  Inoperable or metastatic HR-positive, HER2-negative breast cancer (per ASCO/CAP guidelines, on local laboratory results); ie, is documented as HR-positive (either ER and/or PgR positive [ER or PgR ≥ 1%]) and HER2-negative. If a participant had multiple results after metastatic disease, the most recent local test result will be used to confirm eligibility.  Progressed on or not suitable for endocrine therapy per investigator assessment, and treated with 1 to 2 lines of prior standard of care chemotherapy in the inoperable/metastatic setting. Participant must have documented progression on their most recent line of chemotherapy.  Note: If a chemotherapy drug is changed within 28 days of use to another drug in the same class (ie, antimetabolite to antimetabolite) for any reason, the first drug is not counted as a line. Targeted agents (such as mTOR inhibitors, PD-1/PD-L1 inhibitors, PARP inhibitors), endocrine therapies, and CDK4/6 inhibitors on their own do not contribute to the count of prior lines of chemotherapy; however, regimens with such agents in combination with metastatic chemotherapy should be classified as one line of chemotherapy.  Eligible for one of the chemotherapy options listed as ICC (eribulin, capecitabine, vinorelbine, gemcitabine), per investigator assessment. Note: Participants who previously received any of these agents are eligible for enrolment to another ICC agent in this study. ECOG PS of 0 or 1, with no deterioration over the previous 2 weeks prior to day of first dosing.  At least 1 measurable lesion not previously irradiated that qualifies as a RECIST 1.1. Target Lesion at baseline and can be accurately measured at baseline as ≥ 10 mm in the longest diameter (except lymph nodes, which must have short axis ≥ 15 mm) with CT or MRI, which is suitable for accurate repeated measurements.  Note: Participants with bone-only metastases are not permitted.  Participants with a history of previously treated neoplastic spinal cord compression, or clinically inactive brain metastases, who require no treatment with corticosteroids or anticonvulsants, may be included in the study, if they have recovered from the acute toxic effect of radiotherapy. A minimum of 2 weeks must have elapsed between the end of radiotherapy and study enrolment.  Adequate organ and bone marrow function within 7 days before day of first dosing as follows:  Hemoglobin: ≥ 9.0 g/dL. Red blood cell/plasma transfusion is not permitted within 1 week prior to screening assessment. Absolute neutrophil count: ≥ 1500/mm3. Granulocyte colony-stimulating factor administration is not permitted within 1 week prior to screening assessment. Platelet count: ≥ 100000/mm3. Platelet transfusion is not permitted within 1 week prior to screening assessment. Total bilirubin: ≤ 1.5 × ULN if no liver metastases; or ≤ 3 × ULN in the presence of documented Gilbert's syndrome (unconjugated hyperbilirubinemia) or liver metastases at baseline. ALT and AST: ≤ 2.5 × ULN for AST/ALT; however, if elevation is due to liver metastases, ≤ 5.0 × ULN is allowed. Calculated creatinine clearance: ≥ 30 mL/min as calculated using the Cockcroft- Gault equation (using actual body weight): Female: CrCl = Weight (kg) × (140 - Age) × 0.85 (mL/min) 72 × serum creatinine (mg/dL). Male: CrCl = Weight (kg) × (140 - Age) (mL/min) 72 × serum creatinine (mg/dL) INR or PT, and either PTT or aPTT: ≤ 1.5 × ULN. LVEF ≥ 50% by either an echocardiogram or MUGA within 28 days of first dosing.  Has had an adequate treatment washout period before Cycle 1 Day 1, defined as:  Major surgery: ≥ 3 weeks. Radiation therapy including palliative radiation to chest: ≥ 4 weeks (palliative radiation therapy to other areas ≥ 2 weeks). Anticancer therapy including hormonal therapy: ≥ 3 weeks (for small molecule targeted agents: ≥ 2 weeks or 5 half-lives, whichever is longer) Antibody-based anticancer therapy: ≥ 4 weeks with the exception of receptor activator of nuclear factor kappa-B ligand (RANKL) inhibitors (eg, denosumab for the treatment of bone metastases) Chloroquine/hydroxychloroquine: > 14 days.  All participants must have available a FFPE tumor sample (block preferred, or a minimum of 20 freshly cut slides), at the time of screening. This can be from either the primary disease setting (surgical resection or diagnostic sample), or from a metastatic lesion (excluding bone) for tissue-based analysis (including but not restricted/limited to IHC staining of potential predictive biomarkers as well as tumor mutational analysis). The mandatory FFPE tumor sample submitted for analysis should be obtained as close to the time of diagnosis of metastatic or inoperable disease as possible. If neither an adequate FFPE block nor the minimum of 20 slides are available, a patient may still be considered eligible. In this situation, approval by the Study Team for patient's entry into the study is required.  Note: Sample collection in China will comply with local regulatory approval.  Minimum life expectancy of 12 weeks at screening.  Sex  Male or female. Contraceptive use by men or women should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies; however, oral estrogens are not permitted.  Reproduction  Negative pregnancy test (urine and/or serum) for women of childbearing potential.  Female participants must be post-menopausal for at least 1 year, surgically sterile, or using one highly effective form of birth control (a highly effective method of contraception is defined as one that can achieve a failure rate of less than 1% per year when used consistently and correctly). Women of childbearing potential who are sexually active with a nonsterilized male partner must agree to use one highly effective method of birth control. They should have been stable on their chosen method of birth control for a minimum of 3 months before entering the study to at least 7 months after the last dose.  Female participants must refrain from egg cell donation and breastfeeding while on study and for at least 7 months after the last dose of study intervention. Non-sterilized male partners of a woman of childbearing potential must use a male condom plus spermicide (condom alone in countries where spermicides are not approved) throughout this period.  Male participants who intend to be sexually active with a female partner of childbearing potential must be surgically sterile or using an acceptable method of contraception from the time of screening throughout the total duration of the study and the drug washout period (at least 4 months after the last dose of study intervention) to prevent pregnancy in a partner. Male participants must not donate or bank sperm during this same time period. Not engaging in heterosexual activity (sexual abstinence) for the duration of the study and drug washout period is an acceptable practice if this is the preferred usual lifestyle of the participant; however, periodic or occasional abstinence, the rhythm method, and the withdrawal method are not acceptable methods of contraception.  Informed Consent  Capable of giving signed informed consent as described in Appendix A, which includes compliance with the requirements and restrictions listed in the ICF and in this protocol. Provision of signed and dated written Optional Genetic Research Information informed consent prior to collection of sample for optional genetic research that supports Genomic Initiative.  5.2 Exclusion Criteria Medical Conditions  As judged by the investigator, any evidence of diseases (such as severe or uncontrolled systemic diseases, uncontrolled hypertension, history of allogeneic organ transplant, and active bleeding diseases, ongoing or active infection, or significant or cardiac or psychological conditions) which, in the investigator's opinion, makes it undesirable for the participant to participate in the study or that would jeopardize compliance with the protocol. 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. Exceptions include basal cell carcinoma of the skin and squamous cell carcinoma of the skin that has undergone potentially curative therapy, adequately resected non-melanoma skin cancer, curatively treated in situ disease, or other solid tumors curatively treated. Persistent toxicities caused by previous anticancer therapy (excluding alopecia), not yet resolved to CTCAE Version 5.0 Grade ≤ 1 or baseline. Participants with irreversible toxicity that is not reasonably expected to be exacerbated by study intervention may be included (eg, hearing loss) after consultation with the AstraZeneca study physician or designee. Participants with chronic, stable Grade 2 toxicities (defined as no worsening to > Grade 2 for at least 3 months prior to first dosing and managed with SoC treatment) may be eligible per the discretion of the investigator after consultation with the sponsor study physician or designee.  Uncontrolled infection requiring IV antibiotics, antivirals, or antifungals; suspected infections (eg, prodromal symptoms); or inability to rule out infections.  Note: Participants with localized fungal infections of skin or nails are eligible.  Known active or uncontrolled hepatitis B or C infection; or positive for hepatitis B or Cvirus based on the evaluation of results of tests for hepatitis B (HBsAg, anti-HBs, anti-HBc, or HBV DNA) or hepatitis C (HCV antibody or HCV RNA) infection at screening.  Note: Participants who have received hepatitis B vaccination with only anti-HBs positivity and no clinical signs of hepatitis, and participants who have been curatively treated for hepatitis C infection (as demonstrated clinically and by viral serologies) are eligible.  Known HIV infection that is not well controlled. All of the following criteria are required to define an HIV infection that is well controlled: undetectable viral RNA load, CD4+ counts/levels > 250, no history of AIDs-defining opportunistic infection within the past 12 months, and stable for at least 4 weeks on same anti-HIV retroviral medications. Uncontrolled or significant cardiac disease, including myocardial infarction or uncontrolled/unstable angina within 6 months prior to C1D1, CHF (New York Heart Association Class II to IV), uncontrolled or significant cardiac arrhythmia, or uncontrolled hypertension (resting systolic blood pressure > 180 mmHg or diastolic blood pressure > 110 mmHg).  Investigator judgment of 1 or more of the following:  Mean resting corrected QTcF interval > 470 ms, obtained from triplicate ECGs performed at screening. History of QT prolongation associated with other medications that required discontinuation of that medication, or any current concomitant medication known to prolong the QT interval and cause Torsades de Pointes. Congenital long QT syndrome, family history of long QT syndrome, or unexplained sudden death under 40 years of age in first-degree relatives.  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.  Note: Participants found to have ILD/pneumonitis on baseline screening chest CT are not eligible.  Clinically severe pulmonary compromise resulting from intercurrent pulmonary illnesses including, but not limited to, any underlying pulmonary disorder (ie, pulmonary emboli within three months of first dosing, severe asthma, severe COPD, restrictive lung disease, pleural effusion etc), or any autoimmune, connective tissue or inflammatory disorders with pulmonary involvement (ie, Rheumatoid arthritis, Sjogren's, sarcoidosis etc), or prior pneumonectomy. Leptomeningeal carcinomatosis. Clinically significant corneal disease.  Known active tuberculosis infection (clinical evaluation that may include clinical history, physical examination and radiographic findings, or tuberculosis testing in line with local practice).  Prior/Concomitant Therapy  Any of the following prior anticancer therapies:  Any treatment (including ADC) containing a chemotherapeutic agent targeting topoisomerase I TROP2-targeted therapy Prior treatment with same ICC agent (Note: Participants are eligible for enrolment into this study if they able to receive treatment with another ICC agent not previously received; see Inclusion Criterion 4) Any concurrent anticancer treatment, with the exception of bisphosphonates, denosumab, for the treatment of bone metastases. Concurrent use of hormonal therapy for non-cancer-related conditions (eg, hormone replacement therapy, except topical). Major surgical procedure (excluding placement of vascular access) or significant traumatic injury within 3 weeks of the first dose of study intervention or an anticipated need for major surgery during the study. Receipt of live, attenuated vaccine within 30 days prior to the first dose of study treatment.  Concomitant use of chronic systemic (IV or oral) corticosteroids or other immunosuppressive medications except for managing adverse events (inhaled steroids or intra articular steroid injections are permitted in this study).  Note: Participants with bronchopulmonary disorders who require intermittent use of bronchodilators (such as albuterol) will not be excluded from this study.  Prior/Concurrent Clinical Study Experience  Previous treatment in the present study. Participation in another clinical study with a study intervention or investigational medicinal device administered in the last 4 weeks prior to first dosing, randomization into a prior T-DXd (trastuzumab deruxtecan) study regardless of treatment assignment, or concurrent enrolment in another clinical study, unless it is an observational (noninterventional) clinical study or during the follow-up period of an interventional study. Participants with a known hypersensitivity to Dato-DXd, or any of the excipients of the product (including, but not limited to, polysorbate 80).  Known history of severe hypersensitivity reactions to other monoclonal antibodies.  Other Exclusions  Involvement in the planning and/or conduct of the study (applies to both AstraZeneca staff and/or staff at the study site). Judgment by the investigator that the participant should not participate in the study if the participant is unlikely to comply with study procedures, restrictions and requirements. For women only, currently pregnant (confirmed with positive pregnancy test) or breastfeeding, or who are planning to become pregnant.