A Dose-Escalation Study Evaluating the Combination of Trastuzumab Emtansine (T-DM1) With Neratinib in Women With Metastatic HER2-Positive Breast Cancer

Inclusion Criteria: * The ECOG performance status must be less than or equal to 2. * Patients must have the ability to swallow oral medication. * Patients must have histologic or cytologic confirmation of the diagnosis of invasive adenocarcinoma of the breast. * Patients must have had anti-HER2 based therapy with pertuzumab and trastuzumab for neoadjuvant therapy, adjuvant therapy or with first line therapy for metastatic disease (which may include trastuzumab and pertuzumab either sequentially or in combination). * There must be documentation that the patient has evidence of measurable metastatic breast cancer that is accessible to biopsy at study entry. * Patients must have estrogen receptor (ER) analysis performed prior to study entry. If ER analysis is negative, then progesterone receptor (PgR) analysis must also be performed. (Patients are eligible with either hormone receptor-positive or hormone receptor-negative tumors.) * Breast cancer must be determined by local testing to be human epidermal growth factor receptor 2 (HER2)-positive prior to study entry using American Society of Clinical Oncology (ASCO) - College of American Pathologists (CAP) HER2 test guidelines. * At the time of study entry, blood counts performed within 4 weeks prior to study entry must meet the following criteria: * absolute neutrophil count (ANC) must be greater than or equal to 1000/mm3; * platelet count must be greater than or equal to 100,000/mm3; and * hemoglobin must be greater than or equal to 9 g/dL. (Note: Patient must have discontinued growth factors greater than or equal to two weeks prior to entry labs.) * The following criteria for evidence of adequate hepatic function performed within 4 weeks prior to study entry must be met: * Total bilirubin must be less than or equal to 1.5 x upper limit of normal (ULN), and * aspartate aminotransferase (AST) and alanine aminotransferase (ALT) must be less than or equal to 1.5 x ULN for the lab or less than or equal to 5 x ULN if liver metastasis. * Serum creatinine performed within 4 weeks prior to study entry must be less than or equal to 1.5 x ULN for the lab. * The left ventricular ejection fraction (LVEF) assessment by 2-D echocardiogram or multi-gated acquisition (MUGA) scan performed within 90 days prior to study entry must be greater than or equal to 50% regardless of the facility's lower limit of normal (LLN). * Patients with reproductive potential must agree to use an effective non-hormonal method of contraception during therapy, and for at least 7 months after the last dose of study therapy. Exclusion Criteria * Previous therapy with T-DM1 or any HER2 tyrosine kinase inhibitor (TKI) including neratinib for any malignancy. * Symptomatic brain metastases or brain metastases requiring chronic steroids to control symptoms. * Active hepatitis B or hepatitis C with abnormal liver function tests; HIV positive patients receiving antivirals. * Lung disease resulting in dyspnea at rest. * Active infection or chronic infection requiring chronic suppressive antibiotics. * Malabsorption syndrome, ulcerative colitis, inflammatory bowel disease, resection of the stomach or small bowel, or other disease or condition significantly affecting gastrointestinal function. * Persistent greater than or equal to grade 2 diarrhea regardless of etiology. * Conditions that would prohibit intermittent administration of corticosteroids for T-DM1 premedication. * Chronic daily treatment with corticosteroids with a dose of greater than or equal to 10 mg/day methylprednisolone equivalent (excluding inhaled steroids). * Uncontrolled hypertension defined as a systolic BP greater than 150 mmHg or diastolic BP greater than 90 mmHg, with or without anti-hypertensive medications. (Patients with hypertension that is well controlled on medication are eligible.) * Cardiac disease (history of and/or active disease) that would preclude the use of any of the drugs included in the treatment regimen. This includes but is not confined to: * Active cardiac disease: symptomatic angina pectoris within the past 90 days that required the initiation of or increase in anti-anginal medication or other intervention; ventricular arrhythmias except for benign premature ventricular contractions; supraventricular and nodal arrhythmias requiring a pacemaker or not controlled with medication; conduction abnormality requiring a pacemaker; valvular disease with documented compromise in cardiac function; and symptomatic pericarditis * History of cardiac disease: myocardial infarction documented by elevated cardiac enzymes or persistent regional wall abnormalities on assessment of left ventricular (LV) function; history of documented congestive heart failure (CHF); and documented cardiomyopathy * Other nonmalignant systemic disease that would preclude the patient from receiving study treatment or would prevent required follow up. * Pregnancy or lactation at the time of study entry. (Note: Pregnancy testing should be performed within 14 days prior to study entry according to institutional standards for women of childbearing potential.) * The investigator should assess the patient to determine if she has any psychiatric or addictive disorder or other condition that, in the opinion of the investigator, would preclude her from meeting the study requirements. * Use of any investigational agent within 4 weeks prior to study entry.