• A patient will be eligible for inclusion in this study if she meets all of the following criteria:

‣ Female patients ≥18 years of age

⁃ Have a diagnosis of metastatic TNBC previously treated with standard anthracycline, cyclophosphamide, and taxane chemotherapy, unless there was a contraindication to doxorubicin, in which case prior treatment with this agent is not required. NOTE: TNBC defined as ER-negative tumors with \< or = 10% tumor nuclei immunoreactivity, or ER Low Positive as defined by the updated ASCO/CAP guidelines 2020.

⁃ Have not received more than 3 prior chemotherapy regimens for metastatic disease. Prior platinum and/or taxane therapy in the adjuvant or metastatic setting is permitted.

⁃ Have locoregional (eg, breast, chest wall, regional lymphatic) or pulmonary or hepatic metastatic disease that is amenable to core needle biopsy. If a research biopsy from a patient's metastatic disease cannot be safely obtained, a skin biopsy is permitted. If a skin biopsy cannot be safely obtained, patients may still be eligible, per physician discretion.

⁃ Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 (See Appendix I)

⁃ Have adequate hematologic function, defined by:

• Absolute neutrophil count (ANC) \>1500/μL

∙ Platelet count ≥100,000/μL

∙ Hemoglobin ≥9 g/dL or ≥5.6 mmol/L

⁃ Have adequate liver function, defined by:

• AST and ALT ≤2.5 x the upper limit of normal (ULN) or ≤5 x ULN in presence of liver metastases

∙ Total bilirubin ≤1.5 x ULN OR direct bilirubin ≤ULN for patients with total bilirubin levels \>1.5 × ULN

⁃ Have adequate renal function, defined by:

‣ a. Serum creatinine ≤1.5 x ULN or calculated creatinine clearance of ≥30 mL/min

⁃ Have adequate coagulation function, defined by:

• International Normalized Ratio (INR) OR prothrombin time (PT) and activated partial thromboplastin time (aPTT) ≤1.5 × ULN.

∙ If patient is receiving anticoagulant therapy, PT or aPTT must be within therapeutic range of intended use of anticoagulants.

‣ Patients who have a history of brain metastasis are eligible for the study provided that all the following criteria are met:

⁃ Brain metastases which have been treated

• Off-treatment with steroids for 2 weeks before administration of the first dose of bortezomib

• No ongoing requirement for dexamethasone or anti-epileptic drugs

• No clinical or radiological evidence of progression of brain metastases

‣ Patient must be accessible for treatment and follow-up.

‣ All patients must be able to understand the investigational nature of the study and give written informed consent prior to study entry.