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

Inclusion Criteria: * Participants must have histologically or cytologically confirmed invasive breast cancer with unresectable locally advanced or metastatic disease. Participants without pathologic or cytologic confirmation of metastatic disease should have unequivocal evidence of metastasis from physical examination or radiologic evaluation; i.e., visible chest wall disease or metastases on imaging meeting standard radiology criteria (i.e., lymph nodes larger than 1 cm in the short axis diameter). * The most recent pathology results will be considered for enrollment according to local testing of ER, PR and HER2 in a CLIA-certified environment. ER, PR and HER2 status per local testing must be known prior to study registration. * Participants must have history of HER2-low or HER2-0 breast cancer per local testing, and no known history of HER2-positive breast cancer. All available prior HER2 pathology results must be HER2-low or HER2-0; no known HER2 IHC 3+ or ISH-amplified breast cancer is allowed. * HER2-low status is defined as IHC 1+ or 2+/ISH non-amplified breast cancer in any prior tumor sample (e.g., primary or metastatic tumor) collected prior to study enrollment: IHC 2+/ISH-, IHC 1+/ISH-, or IHC 1+/ISH untested (note: ISH may be determined by either fluorescence in situ hybridization \[FISH\] or dual in situ hybridization \[DISH\]) * HER2-0 status is defined as IHC 0 (null or ultra-low) in all prior tumor samples with available HER2 pathology results: IHC 0+/ISH- or IHC 0+/ISH untested (IHC 0+: IHC 0 absent membrane staining \[null\] or IHC 0 with membrane staining \>0 and \<1+ \[ultralow\]). Note: Enrollment of patients with HER2-0 breast cancer will be capped at 15% in each ADC1 and ADC2 cohort. * Participants with any HR status will be allowed on study. * HR-positive cohorts: ER and/or PR expression ≥1% * HR-negative cohorts: ER and PR expression \<1% * All cohorts: The most recent HER2 pathology result must be HER2-0 or HER2-low (i.e., must not be HER2-positive). * HER2-0: IHC 0+/ISH- or IHC 0+/ISH untested. * HER2-low: IHC 2+/ISH-, IHC 1+/ISH-, or IHC 1+/ISH untested (note: ISH may be determined by either fluorescence in situ hybridization \[FISH\] or dual in situ hybridization \[DISH\]). * Participants must have measurable disease per RECIST 1.1. * Participants must be willing to undergo research tissue biopsies (at baseline prior to ADC1, after 3 weeks of treatment with ADC1, at progression on ADC1 or baseline prior to ADC2, and at progression on ADC2), if tumor is safely accessible. * Prior endocrine therapy: Participants with HR-positive breast cancer considered to be candidates for endocrine therapy must have: a) progressed on or within 12 months of adjuvant endocrine therapy or received at least one line of endocrine therapy in the metastatic setting, and b) received prior CDK4/6 inhibitor. Prior endocrine therapy does not require washout. * Prior chemotherapy: Prior lines of chemotherapy allowed in the metastatic setting are specified below. Prior topoisomerase I inhibitor therapy is not allowed in any setting, except as specified below for ADC2 cohorts. Participants may have discontinued all chemotherapy at least 14 days prior to study treatment initiation. All toxicities related to prior chemotherapy must have resolved to CTCAE v5.0 grade 1 or lower, unless otherwise specified per protocol, except alopecia (any grade allowed) and neuropathy (grade 2 or lower allowed). * ADC1 T-DXd cohorts: Participants must have progressed on 0-1 prior lines in the metastatic setting. * ADC1 Dato-DXd cohorts: Participants must have progressed on 0-1 prior lines in the metastatic setting. * ADC2 T-DXd cohorts: Participants must have progressed on 1-2 prior lines in the metastatic setting, including Dato-DXd (single-agent) as the most recent therapy. Confirmation of documented progressive disease on Dato-DXd (single-agent) as the most recent therapy is required prior to enrollment. No other topoisomerase I inhibitor is allowed in the metastatic setting. * ADC2 Dato-DXd cohorts: Participants must have progressed on 1-2 prior lines in the metastatic setting, including T-DXd (single-agent) as the most recent therapy. Confirmation of documented progressive disease on T-DXd (single-agent) as the most recent therapy is required prior to enrollment. No other topoisomerase I inhibitor is allowed in the metastatic setting. * Prior biologic or targeted therapy: Patients must have discontinued all biologic or targeted therapy (e.g., CDK4/6 inhibitor) at least 14 days prior to study treatment initiation. All toxicities related to prior biologic or targeted therapy must have resolved to CTCAE v5.0 grade 1 or lower, unless otherwise specified per protocol. * Prior investigational agents for treatment of cancer: Investigational agents must have been discontinued at least 21 days prior to initiation of study therapy. All toxicities related to prior investigational agents must have resolved to CTCAE v5.0 grade 1 or lower, unless otherwise specified per protocol. * Prior radiation therapy: Patients may have received prior radiation therapy. Radiation therapy must be completed at least 14 days prior to the initiation of study treatment (at least 7 days for SRS), and all toxicities related to prior radiation therapy must have resolved to CTCAE v5.0 grade 1 or lower, unless otherwise specified per protocol. A 7-day washout is permitted for palliative radiation (≤ 2 weeks of radiotherapy) to non-CNS disease. * Patients with history of treated CNS metastases are eligible, provided the following criteria are met: * Disease outside the CNS is present. * Prior SRS/SRT or WBRT should be completed ≥ 7 days before study treatment initiation. * Recovery from acute toxicity associated with the treatment to ≤ CTCAE v5.0 grade 1 or baseline (with the exception of alopecia), with no requirement for escalating doses of corticosteroids over the past 7 days. * Patients with new or progressive brain metastases (active brain metastases) or leptomeningeal disease are eligible if the treating physician determines that immediate CNS specific treatment is not required and is unlikely to be required during the first cycle of therapy, there is no requirement for corticosteroids, and the patient is asymptomatic. * Participants on bisphosphonates or RANK ligand inhibitors may continue receiving therapy during study treatment and also may initiate therapy with these agents on study if clinically indicated. * The subject is ≥ 18 years old. * ECOG performance status 0-1 (Karnofsky \> 60%). * Participants must have adequate organ and marrow function within 2 weeks prior to study treatment initiation as defined below: * Absolute neutrophil count ≥1,500/mcL * Platelets ≥ 100,000/mcL * Hemoglobin ≥ 9.0 g/dl * INR/PT/aPTT ≤ 1.5 × ULN unless participant is receiving anticoagulant therapy and PT or aPTT is in therapeutic range of anticoagulant * Total bilirubin ≤ 1.5 × institutional upper limit of normal (ULN) (or ≤ 3.0 x ULN in patients with documented Gilbert's Syndrome) * AST(SGOT)/ALT(SGPT) ≤ 2.5 × institutional ULN or ≤ 5.0 × institutional ULN for participants with documented liver metastases * Serum or plasma creatinine ≤ 1.5 × institutional ULN OR creatinine clearance (as calculated using the Cockcroft-Gault equation) ≥ 30 mL/min/ 1.73m2 for participants with creatinine levels above institutional ULN. * Resolution of all toxicities related to prior anticancer therapy to Grade ≤ 1 or baseline, including toxicities from ADC1 before enrolling to ADC2, unless otherwise specified per protocol. * For T-DXd cohorts, baseline LVEF ≥ 50% prior to registration, as measured by echocardiogram (or multiple-gated acquisition \[MUGA\] scan if an echocardiogram cannot be performed or is inconclusive). * Female subjects of childbearing potential must have a negative serum or urine pregnancy test within 2 weeks prior to study treatment initiation. Childbearing potential is defined as participants who have not reached a postmenopausal state (≥ 12 continuous months of amenorrhea with no identified cause other than menopause) and have not undergone surgical sterilization (removal of ovaries and/or uterus). * Women of childbearing potential (WOCBP) and the female partners of male participants must agree to use an adequate method of contraception. Contraception is required starting with the first dose of study medication through 7 months after the last dose of study medication. * Males who are sexually active with WOCBP must agree to follow instructions for method(s) of contraception for the duration of study treatment and 4 months after the last dose of study treatment. * The participant must be capable of understanding and complying with the protocol and willing to sign a written informed consent document. Exclusion Criteria: * Concurrent use of any other investigational or study agents that are being used to treat the underlying malignancy. * Any prior treatment (including ADC) containing a chemotherapeutic agent targeting topoisomerase I, except as specified per protocol for ADC2 cohorts. * Receipt of live, attenuated vaccine (mRNA and replication deficient adenoviral vaccines are not considered attenuated live vaccines) within 30 days prior to the first exposure to study intervention. * Clinically significant corneal disease. * History of severe hypersensitivity reactions to either trastuzumab deruxtecan or datopotamab deruxtecan or their inactive ingredients. * History of severe hypersensitivity reactions to other monoclonal antibodies. * Major surgery within 2 weeks prior to study treatment initiation. * Uncontrolled, significant intercurrent or recent illness including, but not limited to, ongoing or active infection, uncontrolled non-malignant systemic disease, uncontrolled seizures, or psychiatric illness/social situation that would limit compliance with study requirements in the opinion of the treating investigator. * History of (non-infectious) pneumonitis/interstitial lung disease that required steroids or current pneumonitis/interstitial lung disease, or where suspected ILD/pneumonitis cannot be ruled out by imaging at screening. For ADC2 cohorts, if a participant experienced G1 pneumonitis/ILD with ADC1 (e.g., treated with steroids) with complete resolution of radiographic findings and ability to resume ADC1 within 12 weeks of the scheduled interruption without recurrence of ILD, the participant may enroll to ADC2. * Lung-specific intercurrent clinically significant illnesses including, but not limited to, any underlying pulmonary disorder (i.e., pulmonary emboli within 3 months of the study enrollment, severe asthma, severe chronic obstructive pulmonary disease (COPD), restrictive lung disease, pleural effusion etc.), and any autoimmune, connective tissue or inflammatory disorders with pulmonary involvement (i.e., rheumatoid arthritis, Sjogren's syndrome, sarcoidosis etc.), and prior complete pneumonectomy. * Corrected QT interval (QTcF) prolongation to \> 470 msec (females) or \>450 msec (males). * Any of the following procedures or conditions in 6 months prior to enrollment: coronary artery bypass graft, angioplasty, vascular stent, myocardial infarction, angina pectoris, congestive heart failure (New York Heart Association Functional Classification Grade ≥2), and stroke. * Individuals with a history of a second malignancy are ineligible except for the following circumstances: * Individuals with a history of other malignancies are eligible if they have been disease-free for at least 3 years or are deemed by the investigator to be at low risk for recurrence of that malignancy. * Individuals with the following cancers that have been diagnosed and treated within the past 3 years are eligible: cervical/prostate carcinoma in situ, superficial bladder cancer, non-melanoma cancer of the skin. * Patients with other cancers diagnosed within the past 3 years and felt to be at low risk of recurrence should be discussed with the study principal investigator to determine eligibility. * Known human immunodeficiency virus (HIV) infection that is not well controlled. * Known hepatitis B or C virus infection that is active or uncontrolled. * Active infection, including tuberculosis (clinical evaluation that includes clinical history, physical examination and radiographic findings, and tuberculosis testing in line with local practice). * History or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. * Women who are pregnant or breastfeeding or planning to become pregnant.