A Phase II Trial of Stereotactic Body Radiation Therapy and Fluoroestradiol Positron Emission Tomography in Patients With Oligoprogressive Estrogen Receptor Positive Metastatic Breast Cancer

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Age: ≥ 18 years * Female or male * Eastern Cooperative Oncology Group (ECOG) ≤ 2 * Ability to read and understand English or Spanish for questionnaires * Histologically confirmed ER+ (any progesterone receptor \[PR\] and human epidermal growth factor receptor 2 \[HER2\] status is allowed) metastatic breast cancer * The presence of metastatic breast cancer at the time of study entry with progression in 1-4 lesions (including new lesions). Patients that have disease progression in the breast and/or ipsilateral axilla will be considered to have only 1 site of progression even if multiple nodules/lymph nodes are present. Patients with progression in \> 4 lesions are not allowed. Patients with current progression of malignant pleural effusions, malignant ascites, abdominal carcinomatosis, and/or lymphangitic pulmonary involvement are considered to have \> 4 metastases (Note that patients with a history of these conditions earlier in the disease course with no evidence of progression of these conditions are eligible.) * Evidence of extracranial disease progression in 1-4 discrete lesions will be defined by either of the following: * Progression of disease by Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1 or PET Response Criteria in Solid Tumors (PERCIST) v 1.0 criteria OR * Progression of disease in at least 1 but up to 4 lesions as determined by the patient's treating oncologists such that the treating oncologist recommends changing to the next line systemic therapy. Note that a patient may not technically meet RECIST v 1.1 criteria for disease progression in this setting * SBRT must be feasible for all progressing lesions. Feasibility includes but is not limited to: * All progressing lesions must have distinct borders AND * Progressing lesions may not be located within 3 cm of previously irradiated critical structures such as the spinal cord, brachial plexus, brainstem, stomach, and/or small/large bowel that would render the metastasis unsafe to target with SBRT per the treating radiation oncologist * Patients with prior treated brain metastases that are stable are allowed. Patients must not have intracranial disease progression. Patients with prior or current leptomeningeal disease are not allowed * All progressing lesions must be amenable to stereotactic body radiation therapy to a dose of 30 Gy to 40 Gy in 3 to 5 fractions per the treating radiation oncologist * Women of childbearing potential (WOCBP): Negative urine or serum pregnancy test, If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 1 months after the last dose of protocol therapy. * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) Exclusion Criteria: * Has received at least one line, but not more than three lines, of systemic therapy for metastatic disease * Patients may not have received chemotherapy, radiation therapy, biological therapy, immunotherapy, or other anti-cancer treatment within 7-14 days of the start of study therapy (SBRT) at the discretion of treating physician. Chemotherapy must be held during study therapy and can resume 7-14 days after completion of all study therapy (SBRT) at the discretion of treating physician. (Patients may continue anti-endocrine/hormone therapy before, during and after study therapy at the discretion of the treating medical oncologist.) * Clinically significant uncontrolled illness such that the patient is no longer a candidate for systemic therapy * Prior or concurrent malignancy. Prior malignancies with a low probability of recurrence requiring treatment such as the following are allowed: carcinoma in situ of the cervix, non-melanoma skin cancer, and low grade (Gleason score ≤ 6 = Gleason group 1) localized prostate cancer. Prior malignancies not listed require principal investigator (PI) approval * Patients that have only liver metastases will not be allowed * Females only: Pregnant or breastfeeding * Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)