T-Cell Therapy for Advanced Breast Cancer

Inclusion Criteria: * Patients aged ≥18 years with metastatic breast cancer * Karnofsky performance status ≥70% * Patients with breast cancer that is pathologically confirmed at MSKCC (pathology from outside institutions is acceptable for the screening phase of the protocol) and defined by the following: * HER2 negative (in cases of mixed HER2 results, the most recent pathology results considered reflective of the active cancer will be considered) * Previously treated with at least 1 chemotherapy regimen for metastatic disease and documented progression * Expression of mesothelin must be confirmed by meeting 1 of the following criteria: * Mesothelin expression (\>10% of the tumor expressing mesothelin) by IHC * Elevated serum SMRP levels (\>1.0 nM/L) * Presence of measurable or evaluable disease * Chemotherapy, targeted therapy (such as a tyrosine kinase inhibitor), or radiotherapy must have been completed at least 14 days before administration of T-cells. Prior immunotherapy with checkpoint blockade (i.e., PD1 inhibitor, PDL1 inhibitor, or CTL4-antagonist or similar agent) must have been completed more than 1 month before the T-cell infusion. \*Chemotherapy must have been completed at least 7 days prior to leukapheresis * Any major operation must have occurred at least 28 days before study enrollment. * All acute toxic effects of any previous radiotherapy, chemotherapy, or surgical procedures must have resolved to grade 1 or lower according to CTCAE * Lab requirements (hematology): * White blood cell (WBC) count ≥3000 cells/mm\^3 * Absolute neutrophil count ≥1500 neutrophils/mm\^3 * Platelet count ≥100,000 platelets/mm\^3 * Lab requirements (serum chemistry): * Bilirubin \<1.5x upper limit of normal (ULN) * Serum alanine aminotransferase/serum aspartate aminotransferase (ALT/AST) \<5x ULN * Serum creatinine \<1.5x ULN or Cr \>1.5x ULN, but calculated clearances of \>60 * Negative screen for human immunodeficiency virus (HIV), hepatitis B virus (HBV) antigen, and hepatitis C virus (HCV). If testing was performed during the previous 3 months, there is no need to repeat testing, as long as documentation of results is provided to the study site. Subjects must receive counseling and sign a separate informed consent form for HIV testing. * Subjects and their partners with reproductive potential must agree to use an effective form of contraception during the period of drug administration and for 4 weeks after completion of the last administration of the study drug. An effective form of contraception is defined as oral contraceptives plus 1 form of barrier or double-barrier method contraception (condom with spermicide or condom with diaphragm). * Subjects must be able to understand the potential risks and benefits of the study and must be able to read and provide written, informed consent for the study. * Availability of archival tumor tissues (FFPE tissue block or 10-15 unstained slides) Exclusion Criteria: * Untreated or active CNS metastases (progressing or requiring anticonvulsants or corticosteroids for symptomatic control); patients with a history of treated CNS metastases are eligible, provided that all of the following criteria are met: * Presence of measurable or evaluable disease outside of the CNS; * Radiographic demonstration of improvement upon completion of CNS- directed therapy and no evidence of interim progression between completion of CNS-directed therapy and the screening radiographic study; * Completion of radiotherapy ≥8 weeks prior to the screening radiographic study; * Discontinuation of corticosteroids and anticonvulsants ≥4 weeks prior to the screening radiographic study. * History of seizure disorder * Patients currently receiving treatment for concurrent active malignancy. Prior immunotherapy with checkpoint blockade (i.e., PD1 inhibitor, PDL1 inhibitor, or CTL4-antagonist or similar agent) must have been completed more than 1 month prior to the T-cell infusion. * Autoimmune or antibody-mediated disease, including but not limited to systemic lupus erythematosus, rheumatoid arthritis, ulcerative colitis, Crohn's disease, and temporal arteritis (patients with a history of hypothyroidism will not be excluded) * Clinically significant cardiac disease (New York Heart Association class III/IV) or severe debilitating pulmonary disease * Pregnant or lactating women * Known active infection requiring antibiotics within 7 days of the start of treatment (Day 0) * A requirement for daily systemic corticosteroids for any reason or a requirement for other immunosuppressive or immunomodulatory agents. Topical, nasal, and inhaled steroids are permitted. * Administration of live, attenuated vaccine within 8 weeks before the start of treatment (Day 0) and throughout the study * Any other medical condition that, in the opinion of the PI, may interfere with a subject's participation in or compliance with the study * Participation in a therapeutic research study or receipt of an investigational drug within 30 days of T-cell infusion