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 progre