Secondary BRain Metastases Prevention After Isolated Intracranial Progression on Trastuzumab/Pertuzumab or T-DM1 in Patients With aDvanced Human Epidermal Growth Factor Receptor 2+ brEast Cancer With the Addition of Tucatinib

Inclusion Criteria: Subject must meet all of the following applicable inclusion criteria to participate in this study: * Written informed consent and HIPAA authorization for release of personal health information prior to registration. NOTE: HIPAA authorization may be included in the informed consent or obtained separately. * Age ≥ 18 years at the time of consent. * Eastern Cooperative Oncology Group (ECOG) Performance Status of 0-2. * Locally advanced/unresectable or metastatic breast cancer with presence of brain metastases (Stage IV). * Histologically confirmed HER2+ breast carcinoma by ASCO-CAP guidelines, with HER2+ defined by in situ hybridization (ISH), immunohistochemistry (IHC), or fluorescence in situ hybridization (FISH) methodology on most recent biopsy (primary tissue). * Currently receiving: (1) first-line trastuzumab/pertuzumab with or without endocrine therapy OR (2) second-line T-DM1 in the metastatic setting OR (3) adjuvant trastuzumab-based therapy or T-DM1 with isolated intracranial recurrence. Patients with de novo metastatic disease and brain metastases or isolated metastatic disease to the brain can enroll at time of initiation of trastuzumab/pertuzumab. Induction taxane therapy is not required and need to administer can be determined by the treating physician. Patients on trastuzumab alone are allowed if pertuzumab not tolerated. * Systemic disease otherwise stable per RECIST 1.1 or no evidence of extracranial disease. * Adequate hepatic and renal function and hematologic parameters: * Absolute neutrophil count (ANC) ≥ 1.0 × 109/L * Platelets ≥ 100 × 109/L * Hemoglobin ≥ 9 g/dL * Total serum bilirubin ≤ 1.5 times upper limit of normal (ULN) * Aspartate aminotransferase (AST/SGOT) and alanine aminotransferase (ALT/SGPT) ≤ 2.5 × ULN (or ≤ 5 × ULN if liver metastases are present) * Serum creatinine ≤ 1.5 x ULN or estimated creatinine clearance ≥ 50 mL/min as calculated using the Cockcroft-Gault (CG) equation * Left ventricular ejection fraction (LVEF) ≥ 50%. * Central nervous system inclusion - Based on screening brain magnetic resonance imaging (MRI), patients must have ALL of the following: * Adequate local therapy to existing brain lesions ≥ 5mm including surgical resection and/or stereotactic radiosurgery * Limited to first or second intracranial progression. Third intracranial progression would be considered if \> 12 month interval between second and third intracranial progression. * Time since stereotactic radiosurgery (SRS) is ≥ 7 days prior to first dose of study treatment. * Time since surgical resection is ≥ 14 days prior to first dose of study treatment. * Time since local therapy \< 12 weeks. Patients with de novo metastastic breast cancer presenting with brain metastases may enter following cessation of chemotherapy if within 24 weeks of local therapy to the brain and brain metastases have remained stable based on brain MRI. * Prior radiation is required within 12 weeks of enrollment to at least 1 brain lesion. Other brain lesions under 5mm do not require treatment. NOTE: Relevant records of any CNS treatment including radiation must be available to allow for classification of target and non-target lesions * Females of childbearing potential must have a negative serum pregnancy test at screening. If a urine test is done and it is positive or cannot be confirmed as negative, a serum pregnancy test will be required. NOTE: Females are considered of child bearing potential unless they are surgically sterile (have undergone a hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or they are naturally postmenopausal for at least 12 consecutive months. * Females of childbearing potential and males must be willing to abstain from heterosexual intercourse or to use contraception as outlined in the protocol. Exclusion Criteria: Subjects meeting any of the criteria below may not participate in the study: * Previously been treated with: Lapatinib, neratinib, afatinib, tucatinib or other investigational HER2/epidermal growth factor receptor (EGFR) or HER2 tyrosine kinase inhibitor (TKI) at any time previously (patients treated with adjuvant neratinib allowed if relapse \> 12 months after last dose). * Clinically significant cardiopulmonary disease. * Clinically significant acute infection requiring systemic antibacterial, antifungal, or antiviral therapy including: * tuberculosis (clinical evaluation that includes clinical history, physical examination, and radiographic findings, and TB testing in line with local practice), * hepatitis B (known positive HBV surface antigen (HBsAg) result), * hepatitis C, or * human immunodeficiency virus (positive HIV 1/2 antibodies) NOTE: Patients with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody \[anti-HBc\] and absence of HBsAg) are eligible. Patients positive for hepatitis C (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV RNA. Subjects with HIV/AIDS with adequate antiviral therapy to control viral load would be allowed if they are stable and have been on treatment for ≥ 4 weeks prior to first dose of study drug(s). Subjects with viral hepatitis with controlled viral load would be allowed while on suppressive antiviral therapy. Testing not required. * Unable for any reason to undergo MRI of the brain * Use of a strong cytochrome P450 (CYP)2C8 inhibitor within 5 half-lives of the inhibitor, or a strong CYP3A4 or CYP2C8 inducer within 5 days prior to first dose of study treatment. See protocol. * Central nervous system exclusion - Based on screening brain MRI, patients must not have any of the following: * Ongoing use of systemic corticosteroids for control of symptoms of brain metastases at a total daily dose of \> 2 mg of dexamethasone (or equivalent) * Diffuse leptomeningeal disease or positive CSF cytology; however, discreet dural-based metastases are allowed * Poorly controlled seizures. Defined as seizures that continue to occur despite optimal anticonvulsant medications based on investigator discretion. * History of whole brain radiation therapy * Any untreated brain lesions ≥ 5 mm * Active infection requiring intravenous systemic therapy. * Pregnant or breastfeeding (NOTE: breast milk cannot be stored for future use while the mother is being treated on study). * Patients with a prior or concurrent malignancy within last 3 years whose natural history or treatment has the potential to interfere with the safety or efficacy assessment of the investigational regimen, per treating physician discretion, are not eligible for this trial. * Treatment with any investigational drug within 30 days prior to registration.