Patient description: The patient is a 45-year-old postmenopausal woman with cytologically confirmed breast cancer. A core biopsy revealed a 3 cm invasive ductal breast carcinoma in the left upper outer quadrant. The tumor is HER2-positive and ER/PR negative. Axillary sampling revealed 5 positive lymph nodes. CXR was remarkable for metastatic lesions. The patient is using multivitamins and iron supplements. She does not smoke or consume alcohol. She is not sexually active and has no children. She is a candidate for tumor resection and agrees to do so prior to chemotherapy.

Clinical trial eligibility criteria: eligible ages (years): 18.0-999.0,  Anatomic Stage IA Breast Cancer AJCC v8 Anatomic Stage II Breast Cancer AJCC v8 Anatomic Stage IIA Breast Cancer AJCC v8 Anatomic Stage IIB Breast Cancer AJCC v8 Anatomic Stage III Breast Cancer AJCC v8 Anatomic Stage IIIA Breast Cancer AJCC v8 Anatomic Stage IIIB Breast Cancer AJCC v8 Anatomic Stage IIIC Breast Cancer AJCC v8 HER2 Positive Breast Carcinoma Invasive Breast Carcinoma Multifocal Breast Carcinoma Prognostic Stage I Breast Cancer AJCC v8 Prognostic Stage IA Breast Cancer AJCC v8 Prognostic Stage IB Breast Cancer AJCC v8 Prognostic Stage II Breast Cancer AJCC v8 Prognostic Stage IIA Breast Cancer AJCC v8 Prognostic Stage IIB Breast Cancer AJCC v8 Prognostic Stage III Breast Cancer AJCC v8 Prognostic Stage IIIA Breast Cancer AJCC v8 Prognostic Stage IIIB Breast Cancer AJCC v8 Prognostic Stage IIIC Breast Cancer AJCC v8 Synchronous Bilateral Breast Carcinoma HER2-positive status will be based on pretreatment biopsy material and defined as an immunohistochemistry (IHC) score of 3+ and/or positive by in situ hybridization (ISH) according to current American Society of Clinical Oncology (ASCO) College of American Pathologists (CAP) guidelines. Central testing is not required * Known hormone receptor (HR) status as defined by ASCO/CAP guidelines. Hormone receptor positive status can be determined by either known positive estrogen receptor (ER) or known positive progesterone receptor (PR) status; hormone receptor negative status must be determined by both known negative ER and known negative PR Patients with residual HR-negative, HER2 positive (+) disease in the breast and/or lymph nodes per the surgical pathology report are eligible; however, patients with HR+ HER2+ cancers must have node-positive residual disease per the surgical pathology report in order to qualify for the study. The presence of residual invasive disease in the breast is not mandatory for these patients. Note: The presence of micrometastases in lymph nodes after preoperative therapy counts as residual disease, whereas the presence of isolated tumor cells does not Patients with synchronous bilateral invasive disease are eligible provided both lesions were confirmed to be HER2-positive, and at least one of the lesions meets the outlined above. Multifocal disease is allowed, as long as the largest biopsied breast tumor was HER2-positive Patients with clinical stage T1-4, N0-3 disease at presentation and residual invasive disease postoperatively as defined above are eligible. (Note: Patients with T1a/bN0 tumors are not eligible) Patients must have received neoadjuvant chemotherapy with one of the following regimens: docetaxel/trastuzumab/pertuzumab (THP), paclitaxel/methotrexate/cisplatin (TMP), doxorubicin/cyclophosphamide/paclitaxel/trastuzumab/pertuzumab (AC-TH(P)); docetaxel/carboplatin/trastuzumab/pertuzumab (TCH(P)); fluorouracil/doxorubicin/cyclophosphamide-docetaxel/trastuzumab/pertuzumab (FAC-TH(P)), or fluorouracil/epirubicin/cyclophosphamide-docetaxel/trastuzumab/pertuzumab (FEC-TH(P)). Note: apart from TCHP, where T is docetaxel, treatment with docetaxel or paclitaxel is acceptable Patients may have received =< 2 cycles of T-DM1 in the adjuvant setting. Note: These patients will be randomized to receive a further 14 cycles of T-DM1 and tucatinib/placebo as tolerated. The most recent cycle of T-DM1 should have been administered =< 5 weeks prior to registration * N.B: Both of the following two need to be met for the patient to be eligible for this study An interval of no more than 12 weeks between the completion date of the last definitive treatment (e.g. postoperative chemotherapy or radiation, or if neither given, breast surgical date) and the date of registration Patients must be registered on study within =< 180 days of the date of the most recent definitive breast cancer surgery (not including reconstructive surgery) All systemic chemotherapy should have been completed preoperatively unless participating in EA1181 (CompassHER2 pathologic complete response [pCR]) Toxicities related to prior systemic treatment should have resolved or be at baseline, apart from alopecia and peripheral neuropathy =< grade 1  Prior receipt of T-DM1 in the neoadjuvant setting is not allowed Systemic therapy must have consisted of at least 9 weeks of preoperative taxane and trastuzumab (or Food and Drug Administration [FDA]-approved biosimilar) with or without pertuzumab. Patients who have received at least 9 weeks of preoperative taxane, pertuzumab and margetuximab are also eligible. Note: Patients who complete at least nine of a planned twelve doses of weekly paclitaxel, or three of a planned four doses of docetaxel, but discontinue prematurely due to toxicity (i.e. peripheral neuropathy =< grade 1) are eligible. Patients receiving dose-dense chemotherapy regimens are also eligible. Prior use of nab-paclitaxel (Abraxane) instead of paclitaxel or docetaxel is permitted. Prior use of subcutaneous trastuzumab (Hylecta) is also allowed Patients who received neoadjuvant systemic therapy which included experimental HER2-targeted therapy/therapies are potentially eligible, as long as the investigational agent was not a HER2-targeted antibody-drug conjugate (e.g. T-DM1, DS-8201a [trastuzumab deruxtecan]) or a HER2 targeted tyrosine kinase inhibitor (TKI) (e.g. tucatinib, lapatinib, neratinib) No adjuvant treatment with any anti-cancer investigational drug within 28 days prior to registration Not pregnant and not nursing, because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects. Therefore, for women of childbearing potential only, a negative serum pregnancy test done =< 7 days prior to registration is required Patients with known active and/or untreated hepatitis B or hepatitis C or chronic liver disease are ineligible. Patients with a diagnosis of hepatitis B or C that has been treated and cleared and normal liver function are eligible to participate in the study if the other parameters are met Stage IV (metastatic) breast cancer History of any prior (ipsi or contralateral) invasive breast cancer within 3 years of registration Patients with ER+ HER2+ residual invasive disease that is lymph node-negative per the surgical pathology report