SOC Chemotherapy +/- Tocilizumab for Triple Negative and ER-low Breast Cancers

Inclusion Criteria: 1. ≥ 18 years old at the time of informed consent 2. Ability to provide written informed consent and HIPAA authorization 3. Locally recurrent (not amenable to local therapy with curative intent) or metastatic breast cancer that is triple negative or ER-low (ER and PR ≤ 9% weak staining) 4. Received up to 2 prior therapies for metastatic disease 1. Prior (neo)adjuvant therapy will be considered one line of therapy for metastatic disease in patients who recur while on or within 12 months of completion of (neo)adjuvant therapy. 2. Participation in this protocol as either first, second and third-line therapy is allowed. 5. Planned standard of care chemotherapy based on NCCN guidelines. 1. Single agent therapy is preferred but use of combination regimens considered SOC by NCCN is allowed. 2. Chemotherapy delivered via a SOC antibody-drug conjugate is allowed but ADCs may not be used in combination with other agents. 6. Patients with tumors that are PD-L1+ (CPS \> 10) must have had prior exposure to an immune checkpoint inhibitor in the metastatic setting. 1. Patients who received (neo)adjuvant IO therapy and progress while on or within 12 months of completion of (neo)adjuvant IO therapy may participate without additional IO treatment. 2. Patients with major contraindications to immune therapy, may participate without IO exposure regardless of PD-L1 status in the first line setting. 3. PD-L1 status is not required for patients in the second line setting. 7. Measurable disease based on RECIST 1.1 criteria. 8. ECOG PS 0 or 1 9. Patients with treated, asymptomatic CNS disease may participate if the patient is \> 4 weeks from completion of CNS therapy (radiation and/or surgery), is clinically stable at the time of study entry, and is receiving stable or decreasing dose of corticosteroids. Brain MRI or head CT is required at screening for patients with known brain metastases. 10. Adequate organ function as indicated by: 1. Total bilirubin \< ULN (except in patients with documented Gilbert's disease, who must have a total bilirubin \< 3.0 mg/dL) 2. Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 5.0 x ULN 3. Creatinine clearance of \> 50 mL/min using the Cockcroft-Gault formula 4. Absolute neutrophil count (ANC) \> 1.2 K/mm3 5. Platelets \> 75 K/ mm3 6. Hgb \> 9.0 g/dL 11. Women of childbearing potential must have a negative pregnancy test within 14 days of protocol registration. Women are considered to have childbearing potential (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) unless they meet one of the following criteria: 1. Has undergone a hysterectomy or bilateral oophorectomy; or 2. Has been naturally amenorrheic for at least 24 consecutive months. 12. Women of childbearing potential and men must agree to use effective contraception throughout the study and for 6 months after the last study treatment. NOTE: Acceptable methods of birth control include abstinence, partner with previous vasectomy, placement of an intrauterine device (IUD), condom with spermicidal foam/gel/film/cream/suppository, diaphragm or cervical vault cap, or hormonal birth control (pills or injections). Exclusion Criteria: 1. Prior treatment with or known contraindication to treatment with tocilizumab or other IL-6/IL-6R targeted agent 2. Active infection requiring parenteral antibiotics 3. Concurrent use of methotrexate or systemic corticosteroids other than stable or decreasing doses for management of CNS involvement 4. Active or symptomatic CNS disease 5. Patients with HER2+ disease Note: HER2 will be considered positive if scored 3+ by immunohistochemistry (IHC) or 2+ by IHC associated with a fluorescence in situ hybridization (FISH) ratio of \> 2.0 or \> 6 total HER2 gene copies per cell. 6. Patients with active malignancy other than breast cancer. Patients with prior malignancies without recurrence after standard treatment will not be excluded 7. Radiation therapy within 2 weeks of registration 8. Hormone therapy within 2 weeks of registration 9. Planned treatment with Olaparib or other PARP inhibitor.