The purpose of this research study is to determine how well neratinib works in treating breast cancer that has spread to the brain. Neratinib is a recently discovered oral drug that may stop breast cancer cells from growing abnormally by inhibiting (or blocking) members of a family of proteins that include Human Epidermal Growth Factor Receptor 2 (HER2).

In this research study, the investigators are looking to see how well neratinib works to decrease the size of or stabilize breast cancer that has spread to the brain. The investigators are also looking at how previous treatments have affected your thinking (or cognition) and how much neratinib reaches the central nervous system.

Subjects will receive neratinib and a drug-dosing calendar for each treatment cycle. This drug is given orally on a daily basis, continuously. Each treatment cycle will last for 4 weeks during which time the subject will be taking neratinib every day.

• Physical Exams and vital signs: At the start of each cycle, you will have a physical exam. You will be asked questions about your general health and specific questions about any problems that you might be having and any medications you may be taking. You will also have a neurological examination to assess for neurological symptoms.
• Scans (or Imaging tests): We will assess your tumor by brain MRI every 2 cycles ( 6 to 8 weeks) and then every 3 cycles (9 to 12 weeks). CT or MRI scans of your chest, abdomen, and pelvis will be performed every other cycle, at the same time points as the brain MRI. Your research doctor may ask you to have a bone scan at the same time points if this is clinically indicated.
• Photographs: Photographs may be taken of your tumor to assess the response of your tumor to the treatment. Care will be taken to ensure these do not reveal your identity.
• MUGA or Echo: You will have a MUGA or ECHO done every 12 weeks, so every 3 or 4 treatment cycles, depending on which cohort you are on.
• Blood tests: You will have blood tests done at the beginning of each treatment cycle to check your blood cell counts and how well your organs are functioning. In addition to regular blood tests, we will be collecting 2-3 tablespoons of blood for research prior to your study treatment start.
• Neurocognitive Function: If you have previously received treatment for cancer that has spread to your brain (prior to enrollment on this study), you will be asked to take a battery of tests that assess your cognition (thinking) at the start of the study, after 2 cycles of treatment, and possibly at the end of the study. With these tests, we are trying to better understand how your previous treatments and ongoing treatments affect your memory, attention, learning, and other related skills. These tests will be administered to you by a trained research assistant and may take 30-45 minutes to complete.
• For preoperative patients only: If you are a patient who is planning to have an operation to remove the cancer in your brain, you will have your surgery between 7-21 days after starting neratinib. These tests will allow us to measure of how much drug (neratinib) reaches the central nervous system and will help us understand how well neratinib does this.
• At surgery, a part of your tumor cerebrospinal fluid will be collected to test for levels of neratinib. For the cerebrospinal fluid collection, this may require a lumbar puncture just before your surgery begins (spinal tap) if your neurosurgeon feels he/she cannot collect this fluid easily during your surgery. A lumbar puncture is a test often used to detect tumor cells in your cerebrospinal fluid. In this case, we will collect fluid for testing of cancer cells and will also examine the fluid for neratinib concentrations. This will provide information on how much drug (neratinib) reaches the central nervous system. There will be a separate consent form for this procedure given to you by your neurosurgeon (when applicable). This procedure will be done while you are already under general anesthesia for your surgery. If you have a contraindication to having this procedure or if you wish to refuse to undergo this procedure, you may do so.
• You will also have a blood test on day of surgery to test for levels of neratinib
• You will then resume neratinib once you have recovered from your surgery

After the final dose of the study drug:

You will have a follow-up visit one month after coming off study treatment. During that visit, you will have a physical examination, functional assessment, assessment of any toxicities and current medications, and a neurological examination. If you continue to have ongoing toxicity related to your study treatment, we will continue to follow you until this toxicity resolves. In addition, we will collect about 5-6 tablespoons of blood for research and to measure if a marker for your particular breast cancer exists.

We would like to keep track of your medical condition for up to two years after you stop the study treatment. If you are not seen in follow-up at your participating center (where you enrolled on the study), we would like to follow you by calling you on the telephone or by sending you a letter once a year to see how you are doing. We may also contact your doctor once every 6 months to see how you are doing. Keeping in touch with you and checking your condition every year helps us look at the long-term effects of the research study. If you do not wish to be contacted after you stop the study treatment, you must notify the research study staff of your withdrawal of consent for follow-up

Inclusion Criteria:

• Patients (men or women) must have histologically or cytologically confirmed invasive breast cancer, with metastatic disease. Patients without pathologic or cytologic confirmation of metastatic disease should have unequivocal evidence of metastasis by physical exam or radiologic study.
• Invasive primary tumor or metastatic tissue confirmation of HER2-positive status
• Over-expression by immunohistochemistry (IHC) with score of 3+ (in > 30% of invasive tumor cells) AND/OR HER2 gene amplification (> 6 HER2 gene copies per nucleus or a FISH ratio [HER2 gene copies to chromosome 17 signals] of ≥ 2.0)
• Note: Patients with a negative or equivocal overall result (FISH ratio of < 2.0 or ≤ 6.0 HER2 gene copies per nucleus) and IHC staining scores of 0, 1+, 2+ are not eligible for enrollment
• No increase in corticosteroid dose in the week prior to baseline brain MRI
• Prior trastuzumab and lapatinib therapy are allowed.
• There is no limit to the number of previous lines of therapy (including chemotherapy, trastuzumab, and endocrine therapies)
• No prior therapy with neratinib is allowed
• At least 2 weeks washout period post chemotherapy, any prior protocol therapy, lapatinib, other targeted or biologic therapy, or radiation therapy is required prior to study entry
• No washout is required for hormonal therapy but concurrent hormonal therapy is not allowed for patients on study

Patients with progressive disease (Cohort 1):

• For cohort 1, patients must have new or progressive CNS lesions, as assessed by the patient's treating physician.
• In cohort 1, patients must have measurable CNS disease, defined as at least one parenchymal brain lesion that can be accurately measured in at least one dimension with longest dimension ≥10 mm by local radiology review. Note: measurable non-CNS disease is NOT required for study participation
• It is anticipated that some patients may have multiple progressive CNS lesions, one or several of which are treated with SRS or surgery with residual untreated lesions remaining. Such patients are eligible for enrollment on this study providing that at least one residual (i.e. non-SRS-treated or non-resected) lesion is measurable (≥10 mm).
• Patients who have had prior cranial surgery are eligible, provided that there is evidence of measurable residual or progressive lesions, and at least 2 weeks have passed since surgery. If a patient has surgical resection followed by WBRT, then there must be evidence of progressive CNS disease after the completion of WBRT.
• Patients who have had prior WBRT and/or SRS and then whose prior treated lesions have progressed thereafter are also eligible. In this case, lesions which have been treated with SRS may be considered as target lesions if there is unequivocal evidence, in the opinion of the treating physician, of progression.

Patients with with operable disease (Cohort 2):

• In cohort 2, eligible patients will include those who have CNS disease that is amenable for surgery (typically < 3 brain metastases and with planned resection by neurosurgery). These patients may include those who have received or not received previous treatment(s) for their CNS.
• It is anticipated that that patients who have intracranial disease amenable to surgery will have measurable CNS disease prior to study entry and to resection. However, this is not an eligibility requirement. Measurable disease is also not required to continue on protocol subsequent to surgical resection.
• For patients who undergo surgery, postoperative whole brain radiation therapy will not be allowed while patients are on study (concurrent neratinib and radiation therapy has not been studied and toxicity of this is unknown). Patients will require discontinuation of neratinib if radiation therapy will be administered.

Patient Cohort 3:

-In cohort 3, eligible patients must have measurable Central Nervous System disease. Cohort 3a will have participants with no prior lapatinib therapy. Cohort 3b will have had prior lapatinib therapy.

Exclusion Criteria:

• Not pregnant or breastfeeding
• Participants who have had chemotherapy or radiotherapy (including investigational agents) within 2 weeks prior to entering the study or those who have not recovered adequately from adverse events due to agents administered more than 4 weeks earlier (excluding alopecia). Washout from trastuzumab is not required.
• Participants who are currently receiving any other investigational agents
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to neratinib
• Concurrent use of enzyme-inducing antiepileptic drugs (EIAEDs), including phenytoin, carbamazepine, oxcarbazepine, fosphenytoin, phenobarbital, pentobarbital, or primidone
• Patients who are receiving any cancer-directed concurrent therapy, such as concurrent chemotherapy, radiotherapy, or hormonal therapy while on study. Concurrent treatment with bisphosphonates is allowed but should be started before the first dose of neratinib.
• Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
• More than two seizures over the last 4 weeks prior to study entry
• Patients with known contraindication to MRI, such as cardiac pacemaker, shrapnel, or ocular foreign body
• Those with leptomeningeal metastases as the only site of CNS disease
• Significant malabsorption syndrome or inability to tolerate oral medications
• Any predisposing chronic condition resulting in baseline grade 2 or higher diarrhea

Patient Cohort 4:

- In cohort 4, eligible patients must have measurable Central Nervous System disease. Cohort 4a will have participants with previously untreated brain metastases. Cohort 4b will have participants with progressive brain metastases. Cohort 4c will have participants will have progressive brain metastases and prior T-DM1

Exclusion Criteria:

• Participants who are currently receiving any other investigational agents.
• Participants who have had chemotherapy or radiotherapy (including investigational agents) within 2 weeks prior to entering the study or those who have not recovered adequately from adverse events due to agents administered more than 4 weeks earlier (excluding alopecia). Washout from trastuzumab or hormonal therapy is not required.
• History of severe allergic reactions or intolerability attributed to compounds of similar chemical or biologic composition to neratinib and T-DM1 for Cohorts 4A-4C Concurrent use of enzyme-inducing antiepileptic drugs (EIAEDs), including phenytoin, carbamazepine, oxcarbazepine, fosphenytoin, phenobarbital, pentobarbital, or primidone
• Patients who are receiving any cancer-directed concurrent therapy, such as concurrent chemotherapy, radiotherapy, or hormonal therapy while on study. Concurrent treatment with bisphosphonates and denosumab is allowed for bony metastases but should be started before the first dose of neratinib.
• Any prior treatment with T-DM1 for Cohorts 4A-4B.
• For Cohorts 4A, 4B, and 4C: Patients with myocardial infarction or cardiomyopathy onset within the last 6 months are excluded
• Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
• Active hepatitis B or hepatitis C with abnormal liver function tests
• Active liver disease from autoimmune disorders or sclerosing cholangitis
• Lung disease from etiology other than metastatic breast cancer resulting in dyspnea at rest (4A-4C)
• More than two seizures over the last 4 weeks prior to study entry
• Patients with known contraindication to MRI, such as cardiac pacemaker, shrapnel, or ocular foreign body. However, Head CT with contrast is allowed in place of MRI at baseline and throughout the study if MRI is contraindicated and a participant's CNS lesions are clearly measurable on the head CT.
• Those with leptomeningeal metastases as the only site of CNS disease
• Significant malabsorption syndrome or inability to tolerate oral medications
• Any predisposing chronic condition resulting in baseline grade 2 or higher diarrhea
• Inability to comply with study and/or follow-up procedures
• Individuals with a history of a different active malignancy are ineligible.
• Pregnant women are excluded from this study because neratinib (and other agents on study) is an agent with the potential for teratogenic or abortifacient effects