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

Background: * While 10-20% of breast cancers diagnosed in the U.S. are "triple-negative" (TNBC), the 5-year survival rate among TNBC patients with metastatic disease at diagnosis is 12%, and median survival after recurrence is approximately 24 months, demonstrating clear need for additional therapeutic options. * Patients with metastatic hormone-receptor positive (HR+) breast cancer who develop endocrine-refractory disease (that is, no longer responsive to combinations including endocrine therapy) also suffer from a dearth of therapeutic options beyond cytotoxic chemotherapy, with overall survival after standard of care treatment (as seen across recent trials) often less than 1 year. * Personalized oncology strategies have the potential to identify therapies across multiple cancer types. However, such strategies (which currently use patient DNA sequencing) only select a small subgroup of candidate patients by targeting direct matches in their cancers necessitating approaches that can broaden the pool of patients who may benefit from targeted therapies. * Recent computational approaches are able to leverage additional -omics data, such as whole-transcriptome RNA-seq, and relationships between genes, such as synthetic lethality, to better predict responses to off-label targeted therapy or immunotherapy treatments compared to single-target strategies in retrospective clinical trial data. * This study will apply the use of one such published computational transcriptomics algorithm, ENLIGHT, to prospectively identify therapeutic options for participants with metastatic breast cancer who currently experience limited treatment options. Objectives: * Part A: To assess the feasibility of using the ENLIGHT algorithm to match heavily pretreated participants with metastatic breast cancer to off-label therapies * Part B (If feasibility-run in is met): To assess the objective response rate (ORR) of participants with advanced breast cancer using treatment recommended by the computational transcriptomics algorithm ENLIGHT Eligibility: * Participants must have a histologically confirmed diagnosis of metastatic breast cancer. * Participant tumor subtypes will be enrolled as follows: * TNBC Cohort: TNBC will be defined as estrogen receptor (ER) \< 10% or progesterone receptor (PR) \<10% by immunohistochemistry (IHC). * Endocrine-Refractory Cohort: HR+ (ER positive and/or PR positive). HR+ will be defined as ER \>=10% or PR \>= 10% by IHC. * For both cohorts, HER2 will be considered negative if not amplified as per ASCO-CAP 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). * Participants must have been treated with at least one line of standard systemic therapy after diagnosis of metastatic disease, have progressive disease on their current regimen, and must not be eligible for another approved/standard therapy that has been 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. * Participants must have measurable disease per RECIST v1.1. * Archival tumor (preserved via FFPE) must be available from a biopsy performed within the past 6 months, or participants will need to undergo core biopsy and have at least one amenable tumor for the procedure, to optimize reliability of ENLIGHT results. * Age \>=18 years Design: * This is an exploratory study that uses the ENLIGHT algorithm on whole-exome RNA-seq extracted from FFPE tissue to recommend and prioritize off-label therapies for participants. * FFPE blocks from biopsies performed locally may be submitted if obtained 6 months or less prior to study enrollment, or biopsies may be obtained at the NIH in those participants for whom archival tissue is not available and there is at least one measurable site of disease that is deemed safe to biopsy. * All RNA-seq extraction and sequencing will be performed by the CLIA-certified Laboratory of Pathology at the Center for Cancer Research, National Cancer Institute. * Using the ENLIGHT algorithm to recommend and prioritize possible treatment options will test utility of this algorithm, which leverages RNA-seq, to add to clinical decision support. * While on treatment at the NIH, participants will be asked to provide both blood correlative samples and an optional post-treatment tissue biopsy at day 15 / start of cycle 2 as per their treatment protocol.