This clinical trial studies how well fluorine F 18 fluorthanatrace ([18F]FTT) positron emission tomography (PET) works in imaging patients with breast cancer that has spread from where it first started (primary site) to other places in the body (metastatic) who are receiving standard of care (SOC) poly (ADP-ribose) polymerase (PARP) inhibitors with or without immune checkpoint inhibitors (ICI) to be able to detect clinical response to PARP inhibitor ± ICI treatment. [18F]FTT is a radiotracer that targets and binds to PARP1 which can potentially be used for the imaging of PARP1 expression using PET. Once administered, [18F]FTT targets and binds to PARP1. Upon PET, PARP1-expressing tumor cells can be visualized. PET is an established imaging technique that utilizes small amounts of radioactivity attached to very minimal amounts of tracer, in the case, [18F]FTT. Because some cancers take up [18F]FTT it can be seen with PET. PARP inhibitors work as a targeted therapy by blocking an enzyme involved in repairing cell damage. It may cause tumor cells to die. ICI may help the body's immune system attack the cancer and may interfere with the ability of tumor cells to grow and spread. Combining [18F]FTT with a PET scan may help detect tumor cells better in patients with metastatic breast cancer who are receiving standard of care PARP inhibitors with our without ICI treatment.

OUTLINE: Patients are assigned to 1 of 2 arms.

Arm I: Patients receive [18F]FTT intravenously (IV) and undergo PET scan 60-75 minutes later on day 1 of initiating SOC PARP inhibitor ± ICI therapy and again at 12 weeks. At least 1-7 days later, patients undergo SOC FDG PET/computed tomography (CT) and follow up scans at 12 weeks and 6 months. Patients may also undergo tissue biopsy during screening and during follow up.

Arm II: Patients receive [18F]FTT IV and undergo PET scan 60-75 minutes later on day 1 of initiating SOC PARP inhibitor ± ICI therapy. At least 1-7 days later, patients undergo SOC FDG PET/CT and follow up scans at 12 weeks and 6 months. Patients may also undergo tissue biopsy during screening.

After initial [18F]FTT PET imaging, patients are followed-up to 6 months or until disease progression.

Inclusion Criteria:

• Patients must have histologically confirmed invasive breast cancer with metastatic disease
• Patients must be candidates for treatment with PARP inhibitor as a single agent or for PARP inhibitor in combination with an ICI per treating physician discretion
• Patients must have evaluable disease or at least one measurable lesion that can be assessed at baseline by CT (or magnetic resonance imaging [MRI]) per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1
• Age >= 18 years
• Karnofsky performance status (KPS) >= 50% or Eastern Cooperative Oncology Group (ECOG) performance status 0-2
• Archival tissue (formalin-fixed paraffin-embedded [FFPE]) from at least one metastatic site biopsy should be available prior to study enrollment; if archival tissue is not available, then a metastatic site biopsy will be required during the study screening period
• Patient must be willing to proceed with an on-treatment biopsy of metastatic site if an on-treatment [18F]FTT PET will be performed (at 12 ± 4 weeks after starting PARP inhibitor ± ICI treatment)
• For women of childbearing potential, a negative serum pregnancy test is required within 7 days prior to [18F]FTT PET imaging on day 1. For women who obtain on-treatment (12-week) [18F]FTT imaging, a negative serum pregnancy test will be required within 7 days prior to [18F]FTT PET imaging
• Men and women of reproductive potential need to agree to employ two highly effective and acceptable forms of contraception throughout their participation in the study
• Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations
• Ability to understand and the willingness to sign a written informed consent document. Informed consent must be provided prior to any study specific procedures

Exclusion Criteria:

• Patients with prior myelodysplastic syndrome or acute myeloid leukemia due to rare risk associated with PARP inhibitor therapy
• Pregnant or breastfeeding women
• Patient with a known hypersensitivity to the proposed PARP inhibitor product
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
• Patients unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of PARP inhibitor therapy (per investigator's discretion)