A Synthetic Lethality-Focused Algorithm to Identify Therapeutic Options in Advanced Metastatic Breast Cancer (SYNTHESIS-Breast)

-INCLUSION CRITERIA: 1. Participants must have a histologically confirmed diagnosis of metastatic breast cancer. Note: Pathology testing outside NIH will be accepted for eligibility purposes. 2. Participant tumor subtypes will be enrolled as follows: * TNBC Cohort: TNBC will be defined as ER \< 10% or PR \< 10% by immunohistochemistry (IHC). * Endocrine-Refractory Cohort: HR+ (ER+ and/or PR+) will be defined as ER \>= 10% or PR \>= 10% by IHC. * For both cohorts, HER2 will be considered negative if not amplified as per ASCOCAP guidelines per IHC/FISH. Note: HER2-low status will be regarded in accordance with NCCN guidelines (in which this designation serves as a predictive marker for trastuzumab deruxtecan, but participants are otherwise not considered eligible for other HER2-directed therapies). 3. Participants must have been treated with at least one (1) line of systemic therapy after diagnosis of metastatic disease, have progressive disease or adverse events requiring discontinuation of their current regimen, and must not be able to transition to another approved systemic therapy shown to improve overall survival. -Participants with HR+ disease must be deemed refractory to endocrine therapy per their clinical team, with concordance by study team. Note: Participants who cannot receive standard therapy that has been shown to prolong overall survival due to concurrent medical issues versus progression of disease will be eligible, if other eligibility criteria are met. If appropriate, participants may remain on treatment during biopsy, screening and initial tissue review/testing for this study. However, their clinical team must confirm that the current line of treatment no longer offers benefit prior to the time of reporting and treatment assignment. 4. Participants must have measurable disease per RECIST v1.1. Note: Palliative radiotherapy to site(s) of disease may be completed during screening as long as disease outside of the planned sites of radiation is available for response assessment. 5. Archival tumor (preserved via FFPE) must be available from a biopsy performed within the past 6 months. The timeframe of 6 months is required to optimize reliability of ENLIGHT results. It is assumed that a participant has had no more than one (1) line of systemic treatment since the last biopsy. Participants who have had multiple intervening lines of therapy since biopsy was obtained will be reviewed by the study team to determine if another biopsy may be needed. Note: If archival tissue is not available within that timeframe, tissue from the next scheduled biopsy can be sent to NIH for testing. If it is not possible for a biopsy to be scheduled, the study team will evaluate the possibility of a biopsy being performed at the NIH for enrollment purposes. 6. Age \>=18 years. 7. ECOG performance status \<2 (Karnofsky \>60%) 8. Participants must have organ and marrow function as defined below: * Leukocytes \>= 3,000/mcL * Hemoglobin \>= 8g/dL * Absolute neutrophil count \>= 1,200/mcL * Platelets \>=75,000/mcL * Total bilirubin \<= 1.5 x institutional upper limit of normal (In the case of known Gilbert's Disease, total bili \>1.5 may be considered.) * AST(SGOT)/ALT(SGPT) \<= 3x institutional upper limit of normal * Creatinine \< 1.5 x normal institutional limits OR Creatinine clearance \>=60 mL/min/1.73 m2 9. Ability to take oral medications. 10. Participants with an existing diagnosis of diabetes or hypertension, must have disease well-controlled with at least annual physician follow-up. 11. Women of child-bearing potential and men with a partner of child-bearing potential must be willing to use appropriate contraception in the event that they match to a therapy that requires such. The duration of contraception use will depend on the therapy assigned. 12. Willingness to comply with required study procedures and visits for the duration of study. 13. Participants with asymptomatic brain metastases may be included if metastases have been previously treated with local therapy including radiation at least 4 weeks prior to first dose of treatment and there is no indication for additional local therapy (including active progression). 14. Participants with human immunodeficiency virus (HIV) must be on an effective antiretroviral therapy with undetectable viral load for at least the last 6 months. 15. Participants with evidence of chronic hepatitis B virus (HBV) infection, must have HBV viral load that is undetectable on suppressive therapy, if indicated. 16. Participants with a history of hepatitis C virus (HCV) infection must have been treated and cured. Participants with HCV infection must be currently on treatment, with undetectable HCV viral load. 17. Participants with a prior or concurrent malignancy are eligible if the natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the off-label therapies offered on this study in the opinion of the Principal Investigator (PI) and are otherwise eligible for this trial. 18. Participants with current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. Note: To be eligible for this trial, participants should be class 2B or better. 19. Ability of participant to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA: 1. Participants in active visceral crisis, symptomatic brain metastases requiring local therapy, or active leptomeningeal disease given the time required for testing and therapy selection. 2. Participants with uncontrolled intercurrent illness evaluated by physical exam and chemistries or situations that would limit compliance with study requirements, interpretation of results or that could increase risk to the participant. 3. Participants with the following active cardiac conditions: symptomatic congestive heart failure, unstable angina pectoris or cardiac arrhythmia (per medical record). 4. Participants with lung disease requiring continuous oxygen supplementation. 5. Participants with decompensated cirrhosis and/or end-stage kidney disease on dialysis. 6. Participants with positive serum or urine beta-HCG pregnancy test performed at screening. 7. Participants who are unable to provide tissue specimens of sufficient quality for use in this study. Quality of DNA and RNA is determined during screening. This may be due to issues with biopsy sample collection, inadequate RNA extraction, or quality control failure. Participants may be re-screened if initial specimens are not adequate, if they are amenable to re-biopsy, and additional site(s) of disease for adequate re-sampling are available.