Lutetium-177 DOTATATE for Stage IV or Recurrent Breast Cancer

Inclusion Criteria:

* Life expectancy of \> 6 months, as determined by the investigator
* Ability to understand and the willingness to sign a written informed consent document
* Patients aged \>= 18-100 years old at time of informed consent
* Histologically or cytologically confirmed metastatic breast carcinoma
* Stage IV or recurrent disease with distant metastases
* Female and male patients with breast cancer will be included in the study
* Participants must have experienced disease progression after at least two lines of standard treatment modalities and/or one prior line of cytotoxic chemotherapy (not just endocrine therapy). Specifically, patients must have received or declined the following therapies: a) Hormone receptor positive (HR+)/HER2: endocrine therapy and CDK4/6 inhibitor (i); b) HER2+: trastuzumab, pertuzumab, T-DM1 and tucatinib; c) Triple negative breast cancer (TNBC): chemotherapy, immunotherapy (in PD-L1+ tumors). Patients can be consented if they are foregoing treatments known to confer survival advantage
* Participants must have at least one measurable site of disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) version (v1).1 that is amendable to biopsy
* Confirmed presence of SSTR based on \> 50% of lesions with DOTATATE uptake of 68Ga DOTATATE equivalent to the liver
* Participants must have fully recovered from the acute toxic effects of all prior treatment to grade 1 or less, except alopecia and =\< grade 2 neuropathy which are allowed
* Participant must have Eastern Cooperative Oncology Group (ECOG) performance status =\< 2
* Participant must consent to undergo a pre-treatment screening biopsy for enrollment
* Hemoglobin \>= 8.0 g/dL with no blood transfusion in the past 28 days (measured within 28 days prior to administration of study treatment)
* Absolute neutrophil count (ANC) \>= 2.0 x 10\^9/L (measured within 28 days prior to administration of study treatment)
* Platelet count \>= 75 x 10\^9/L (measured within 28 days prior to administration of study treatment)
* Total bilirubin =\< 3 x institutional upper limit of normal (ULN) (measured within 28 days prior to administration of study treatment)
* Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x institutional upper limit of normal (unless liver metastases are present in which case they must be =\< 5 x ULN) (measured within 28 days prior to administration of study treatment)
* Serum albumin \>= 3.0 g/L, unless prothrombin time or international normalized ratio (INR) value is within the normal range (measured within 28 days prior to administration of study treatment)
* Participants must have serum creatinine =\< 1.7 mg/dL, or creatinine clearance estimated of \>= 51 mL/min using the Cockcroft-Gault equation or based on a 24 hour urine test (measured within 28 days prior to administration of study treatment)
* Female participants of childbearing potential (FOCBP) must have a negative urine or serum pregnancy test within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required
* FOCBP agree to use a highly-effective method of contraception starting with the first dose of study therapy up to 7 months after the last dose of study therapy

  * FOCBP are those who are not proven postmenopausal. Postmenopausal is defined as:

    * Amenorrheic for \> 24 consecutive months following cessation of exogenous hormonal treatments
    * Luteinizing hormone (LH) and Follicle stimulating hormone (FSH) levels in the post menopausal range for women under 50 years of age
    * Radiation-induced oophorectomy with last menses \> 1 year ago
    * Chemotherapy-induced menopause with \> 1 year interval since last menses
    * Surgical sterilization (bilateral oophorectomy or hysterectomy or tubal ligation)

Exclusion Criteria:

* Currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of first dose of 177Lu- DOTATATE treatment

  * Individuals in the follow-up phase of a prior investigational study may participate as long as it has been 4 weeks since last dose of the previous investigational agent or device
* Prior external beam radiation therapy to more than 25% of the bone marrow
* Other malignancy unless curatively treated with no evidence of disease for \>= 5 years except: adequately treated non-melanoma skin cancer or curatively treated in situ cancer of the cervix
* Known brain metastases, unless these metastases have been treated and stabilized
* Peptide receptor radionuclide therapy at any time prior to study enrollment
* Known hypersensitivity to somatostatin analogues or any component of the 68Ga- DOTATATE or 177Lu- DOTATATE formulations
* Patients with uncontrolled infection will not be enrolled until infection is treated per provider discretion
* Uncontrolled intercurrent illness including, but not limited to, symptomatic congestive heart failure, unstable angina pectoris, serious cardiac arrhythmia, myocardial infarction within 6 months prior to enrollment, New York Heart Association (NYHA) class III or IV heart failure
* Uncontrolled diabetes mellitus as defined by a fasting blood glucose \> 2x ULN
* Any patient receiving treatment with short-acting somatostatin analogs, which cannot be interrupted for both 24 hours before and after the administration of 177Lu, or any patient receiving treatment with long-acting release somatostatin analogs that cannot be interrupted for at least 4 weeks before the administration of 177Lu- DOTATATE
* Any surgery or radiofrequency ablation within 12 weeks prior to enrollment in the study; or prior radioembolization; chemoembolization; or external beam radiation therapy (EBRT) to \> 25% of bone marrow, at any time
* Any chemotherapy or targeted therapy within 4 weeks prior to enrollment in the study
* Current spontaneous urinary incontinence making impossible the safe administration of the radioactive study agent
* Any psychiatric illness that prevents patient from informed consent process
* Any concurrent condition that, in the Investigator's opinion, would jeopardize the safety of the patient or compliance with the protocol
* Participant is pregnant or breastfeeding, or expecting to conceive within the projected duration of the trial, starting with the screening visit through 6 months after the last dose of trial treatment