Pembrolizumab With Carboplatin Compared to Carboplatin Alone in Breast Cancer Patients With Chest Wall Disease

Inclusion Criteria: 1. Advanced breast cancer with locally recurrent chest wall disease not amenable to surgical excision with curative intent. 1. Distant sites of disease are allowed 2. Prior radiation to the chest wall is not required 2. The following disease subtypes are eligible: 1. Triple negative disease (defined as ER \< 10%, PR \< 10%, HER2 negative) 2. Hormone receptor positive, HER2 negative disease with evidence of progression on at least two prior lines of hormone therapy, unless, per treating investigator's judgement, is not considered a candidate for further endocrine therapy 3. HER2 positive disease with evidence of disease progression on trastuzumab, pertuzumab, Trastuzumab emtansine (T-DM1), and oral tyrosine kinase inhibitor unless contraindicated with no other HER2 targeted therapy options available. Patients in this category will be classified by ER status * Histologically confirmed HER2+ breast carcinoma, with HER2+ defined by in situ hybridization (ISH) or fluorescence in situ hybridization (FISH) or immunohistochemistry (IHC) methodology using standard criteria. * Cardiac function must be determined within 4 weeks of study entry to be \>= institutional lower limit of normal (LLN) using echo or multiple gated acquisition scan (MUGA). 3. Any number of prior lines of therapy are allowed. a Prior platinum based therapy is allowed in the following settings: * Treatment in the neoadjuvant and/or adjuvant setting without clear progression of disease. * Treatment in the metastatic setting without clear progression of disease. b Neo/adjuvant treatment with a checkpoint inhibitor is allowed if the last treatment was at least 12 months from the diagnosis of metastatic disease. 4. At least two weeks from last systemic therapy for breast cancer, with recovery of all treatment related toxicity to grade 1 or less. Subjects with \<= Grade 2 neuropathy are an exception to this criterion. 5. At least two weeks from last radiation therapy, with recovery of all treatment related toxicity to grade 1 or less (excluding alopecia). 6. Prior CNS disease is allowed if stable for at least one month since whole brain radiation therapy, and 2 weeks since stereotactic radiotherapy, and not requiring steroids. Patients whose CNS disease was surgically treated may be enrolled if stable for at least one month, and not requiring steroids. 7. Able to provide tissue from a newly obtained core or excisional biopsy of a chest wall tumor lesion. Newly-obtained is defined as a specimen any time after the last systemic or local therapy utilized to treat the disease. Subjects for whom newly-obtained samples cannot be provided (e.g. inaccessible or subject safety concern) may submit an archived specimen only upon agreement from the Sponsor. 8. Willing and able to provide written informed consent. 9. Greater than or equal to 18 years of age on day of signing informed consent. 10. Eastern Cooperative Oncology Group (ECOG) performance status of less than or equal to 2. 11. Adequate organ function as defined below within 10 business days of treatment initiation: * Absolute neutrophil count (ANC) \>=1,000 /microliter (mcL) * Platelets\>=100,000 / mcL * Hemoglobin ≥9 g/dL or ≥5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment) * Serum creatinine OR Measured or calculated\* creatinine clearance (GFR can also be used in place of creatinine or CrCl) \<=1.5 X upper limit of normal (ULN) OR \>=60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN. Creatinine clearance should be calculated per institutional standard. * Serum total bilirubin ≤ 1.5 X ULN OR Direct bilirubin \<= ULN for subjects with total bilirubin levels \> 1.5 ULN * Aspartate aminotransferase (AST) (SGOT) and Alanine aminotransferase (ALT) (SGPT) ≤ 2.5 X ULN OR ≤ 5 X ULN for subjects with liver metastases * Albumin \>2.5 g/dL * International Normalized Ratio (INR) or Prothrombin Time (PT) \<=1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants * Activated Partial Thromboplastin Time (aPTT) \<=1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants 12. Female subjects of childbearing potential should have a negative urine or serum pregnancy 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. 13. Female subjects of childbearing potential should be willing to use an acceptable form of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication (Reference Section 5.7.2). Subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year. 14. Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy. Exclusion Criteria: 1. Treatment with an investigational agent within 4 weeks of the first dose of treatment. 2. A diagnosis of immunodeficiency or is currently receiving systemic steroid therapy at any dose or is receiving any other form of immunosuppressive therapy. Steroid therapy is not allowed within 7 days prior to the first dose of trial treatment. However, topical and intranasal corticosteroids are allowed, and not an exclusion for participation. 3. Known active TB (Bacillus Tuberculosis). Patients with a distant history of tuberculosis that was appropriately treated and have no evidence of active infection are eligible to participate. Patients with a history of latent tuberculosis that was appropriately treated are also eligible to participate. 4. Hypersensitivity to pembrolizumab or any of its excipients. 5. Hypersensitivity to carboplatin or cisplatin 6. Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to a previously administered agent. * Note: Subjects with ≤ Grade 2 neuropathy are an exception to this criterion. * Note: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. 7. Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer. 8. Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. 9. Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. 10. Has a history of (non-infectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/ interstitial lung disease 11. Has an active infection requiring systemic therapy. 12. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. 13. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. 14. Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment. 15. Prior checkpoint inhibitor therapy in the metastatic setting. 16. Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies). 17. Has known active Hepatitis B virus (HBV) \[e.g., hepatitis B surface antigen (HBsAg) reactive\] or Hepatitis C virus (HCV) \[e.g., HCV ribonucleic acid (RNA), \[qualitative\] is detected\]. 18. Has received a live vaccine or live-attenuated vaccine within 30 days prior to the first dose of study drug. Administration of killed vaccines is allowed.