A Study Of Pembrolizumab In Combination With Trastuzumab-DM1

Inclusion Criteria: * Patients must have histologically or cytologically confirmed invasive breast cancer, with stage IV disease. Patients without pathologic or cytologic confirmation of metastatic disease should have unequivocal evidence of metastasis from physical examination or radiologic evaluation. * Either the primary tumor and/or the metastasis must have been tested for ER, PR and HER2. Patient must have HER2+ breast cancer per ASCO CAP guidelines 2013. * Prior chemotherapy: * History of prior therapy with trastuzumab and a taxane, separately or in combination, is required. * Patients must have either received one line of prior therapy for metastatic breast cancer, or have developed a disease recurrence during or within 6 months after completing adjuvant therapy. * No prior treatment with T-DM1 is allowed. * Last dose of chemotherapy must be at least 21 days prior to registration. * Prior biologic therapy: --Patients must have discontinued all biologic or investigational therapy at least 21 days before registration. * Prior radiation therapy: * Patients may have received prior radiation therapy in either the metastatic or early-stage setting. * Radiation therapy must be completed at least 14 days prior to registration. * In the dose de-escalation cohort: Subjects must have evaluable disease. In the expansion cohort: Subjects must have at least one lesion that is not within a previously radiated field that is measurable on computerized tomography (CT) or magnetic resonance imaging (MRI) scan per RECIST version 1.1. Bone lesions are not considered measurable by definition. * Age is ≥18 years. * ECOG performance status ≤2 (Karnofsky ≥60%, see Appendix A) * Participants must have normal organ and marrow function as defined below: * absolute neutrophil count ≥1,500/μl * platelets ≥100,000/μl * hemoglobin ≥9 g/dL * total bilirubin ≤1.5mg/dL (≤2.0 in patients with known Gilberts syndrome) * AST(SGOT)/ALT(SGPT) ≤2.5 × institutional ULN. ≤5.0 × institutional ULN for patients with documented liver metastases. * albumin \>2.5mg/dL * serum creatinine ≤1.5mg/dL or calculated GFR ≥60 mL/min * INR/PT ≤1.5 times ULN unless participant is receiving anticoagulant therapy, as long as PT or PTT is within therapeutic range of intended use of anticoagulants * aPTT/PTT ≤1.5 times ULN unless participant is receiving anticoagulant therapy, as long as PT or PTT is within therapeutic range of intended use of anticoagulants * Participants enrolling in the dose expansion must have tissue that is amenable to biopsy and be willing to undergo a fresh tissue biopsy at baseline. Participants who undergo an attempted research biopsy procedure for the purpose of this protocol, and in whom inadequate tissue is obtained, are not required to undergo a repeat biopsy in order to continue on protocol. * The effects of pembrolizumab on the developing human fetus are unknown. For this reason and because tratuzumab, a component of T-DM1, is known to be teratogenic, women of child-bearing potential and men of childbearing potential must agree to use adequate contraception starting with the first dose of study therapy, for the duration of study participation, and for an additional 120 days after the last dose of study medication. Note: abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. * Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, the treating physician and principal investigator should be informed immediately. * While on the study, women should not breast-feed. * Subjects of childbearing potential are defined as those who have not been surgically sterilized and/or have had a menstrual period in the past year * Female subject of child-bearing potential must have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication. If a urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * Patients on bisphosphonates may continue receiving bisphosphonate therapy during study treatment. * Left ventricular ejection fraction (LVEF) must be within institutional limits of normal as assessed by echocardiogram or MUGA documented within 28 days prior to first dose of study drug. * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * The subject has received another investigational agent within 21 days of the first dose of study drug. * The subject has received prior pembrolizumab or any other anti-PD-1 , anti-PD-L1, or anti-PD-L2 therapy, or has participated in any prior studies involving pembrolizumab. * Pre-existing neuropathy greater than or equal to grade 2. * Hypersensitivity to pembrolizumab or T-DM1 or any of their excipients. * The subject has any history or evidence of active, non-infectious pneumonitis or interstitial lung disease. * Known brain metastases that are untreated, symptomatic, or require therapy to control symptoms. Participants with previously diagnosed brain metastases are eligible if they have completed treatment at least one month prior to trial therapy initiation, are neurologically stable with an absence of new neurological symptoms for at least 4 weeks prior to study entry, and have recovered from effects of radiotherapy or surgery. Any corticosteroid use for brain metastases must have been discontinued without the subsequent appearance of symptoms for ≥2 weeks before the first study drug. Treatment for brain metastases may include whole brain radiotherapy, radiosurgery, or a combination as deemed appropriate by the treating physician. * Known carcinomatous meningitis. * The subject has an uncontrolled intercurrent illness including, but not limited to, uncontrolled hypertension, unstable angina pectoris, uncontrolled cardiac arrhythmia, congestive heart failure (New York Heart Association Class III or IV; see Appendix B), active ischemic heart disease, myocardial infarction within the previous six months, uncontrolled diabetes mellitus, chronic liver or renal disease, or severe malnutrition. * Concurrent use of potent CYP3A4 inhibitors (see Appendix C), such as ketoconazole and erythromycin, should be avoided during the study treatment with T-DM1. * Active infection requiring intravenous antibiotics at cycle 1 day 1. * Individuals with a history of a second malignancy are ineligible except for the following circumstances. Individuals with a history of other malignancies are eligible if they have been disease-free for at least 5 years and are deemed by the investigator to be at low risk for recurrence of that malignancy. Individuals with the following cancers are eligible if diagnosed and treated within the past 5 years: cervical cancer in situ, and non-melanoma cancer of the skin. Patients with other cancers diagnosed within the past 5 years and felt to be at low risk of recurrence should be discussed with the study sponsor to determine eligibility. * The subject has a medical condition that requires chronic systemic steroid therapy or any other form of immunosuppressive medication including disease modifiying agents, or has required such therapy in the last 2 years. Replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. * The subject has an active autoimmune disease or a documented history of autoimmune disease or syndrome that requires systemic steroids or immunosuppressive agents. * The participant is positive for Hepatitis B surface antigen, or Hepatitis C RNA. * Known HIV-positive participants. HIV-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with pembrolizumab. In addition, these participants are at increased risk of lethal infections with bone marrow suppressive therapy, i.e. nab-paclitaxel. Appropriate studies will be undertaken in participants receiving combination antiretroviral therapy when indicated. * The subject has received a live vaccine within 28 days of planned start of study therapy. Note: seasonal influenza vaccines for infection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (i.e. Flu-Mist ®) are live attenuated vaccines, and are not allowed