The SAPPHO Study: Sequential Therapy With Curative Intent in de Novo HER2+ Metastatic Breast Cancer

Inclusion criteria: * Participants must have histologically or cytologically confirmed unresectable locally advanced or metastatic invasive breast carcinoma. Patients must have stage IV breast carcinoma at diagnosis (i.e., de novo metastatic) with unequivocal evidence of metastasis on imaging. * Diagnosis of HER2-positive invasive breast carcinoma and 3+ by immunohistochemistry on both breast and metastatic biopsies, as defined by the current American Society of Clinical Oncology - College of American Pathologists (ASCO/CAP) guidelines. HER2 status must be determined at a Clinical Laboratory Improvements Amendments (CLIA)-certified or International Organization for Standardization (ISO)-accredited laboratory (central testing not required). Patients with HER2 1+ or 2+ disease which is HER2 FISH positive are not eligible to enroll. * No prior systemic therapy for invasive breast cancer, aside from first-line trastuzumab/pertuzumab/taxane (THP) within 6 weeks from treatment start. Prior endocrine therapy for non-invasive breast carcinoma or non-cancerous lesions is allowed if it has been completed at least 5 years prior to study entry. * Age ≥18 years. Because no dosing or adverse event data are currently available on the use of trastuzumab, pertuzumab, paclitaxel, trastuzumab deruxtecan, T-DM1 and tucatinib in Participants \<18 years of age, children are excluded from this study, but will be eligible for future pediatric trials. * Eastern Cooperative Oncology Group Performance Status (ECOG PS) 0-1 * Left ventricular ejection fraction (LVEF) ≥50%, as assessed by echocardiogram (ECHO) or multiple-gated acquisition scan (MUGA) documented within 12 weeks prior to first dose of study treatment, or within 12 weeks before starting THP for patients who start metastatic therapy prior to study entry. * Participants must meet the following organ and marrow function as defined below within 28 days prior to registration: * Hgb ≥9.0 g/dL * Absolute Neutrophil Count ≥ 1,000 /mm3 * Platelets ≥100,000/mm3 * Total bilirubin ≤ 1.5 x ULN (institutional) or direct bilirubin within normal limits in patients with a history of Gilbert\'s syndrome. * AST and ALT ≤ 2.5 x ULN (institutional) or ≤ 5 x ULN for participants with documented liver metastases * Serum creatinine ≤ 1.5 x ULN (institutional) OR calculated GFR ≥60mL/min * Participants with concurrent human immunodeficiency virus (HIV) infection are eligible provided the following criteria are met: * CD4+ T-cell (CD4+) counts \> 350 cells/uL * No history of AIDS-defining opportunistic infection within 12 months prior to enrollments * Any medication used in an ART regimen must have no known interaction with the agents used in the study treatment regimen. * Participants with active or chronic Hepatitis B or C are eligible provided they meet the liver function criteria described in 3.1.7 and are not on a medication with a known liver function criteria described in 3.1.7 and are not on a medication with a known interaction with the agents used in the study treatment regimen. The following guidance applies: * patients with chronic HBV infection with active disease who meet the FDA criteria for anti-HBV therapy should be on a suppressive antiviral therapy prior to initiation of cancer therapy. * patients with a history of HCV infection should have completed curative antiviral treatment. HCV viral load must be below the limit of quantification. * patients who are HCV Ab positive but HCV RNA negative due to prior treatment or natural resolution are eligible. * Participants with brain metastases identified at diagnosis or at time of screening are eligible if the following criteria are met: * Known, untreated brain metastases must undergo definitive local therapy - as determined by treating physician - prior to study entry. * Treated brain metastases must be clinically stable since treatment. Restaging brain MRI is not required to deem eligibility if local therapy was given within 28 days from first dose of study treatment. Patients are eligible if time from local therapy and first dose of study treatment is: * 7 days for stereotactic radiosurgery (SRS); * 14 days for whole-brain radiation therapy (WBRT); * 28 days for surgical resection. * Patients who have already started THP prior to study entry and have brain metastasis detected at screening MRI are eligible after completion of definitive local therapy- as determined by treating physician. Systemic treatment can be interrupted as determined by the treating physician and after discussion with the Sponsor Investigator. * Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible (i.e., adequately treated carcinoma in situ of the cervix, non-melanoma skin carcinoma, localized prostate cancer, ductal carcinoma in situ, or Stage I uterine cancer). * This study involves agents that have known genotoxic, mutagenic and teratogenic effects. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her Partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 7 months after completion of study therapy. * Women of childbearing potential must have had a negative pregnancy test within 14 days of registration. Childbearing potential is defined as: those who have not been surgically sterilized and/or have had a menstrual period in the past 12 months or who have been on ovarian suppression in the past year. * Ability to understand and the willingness to sign a written informed consent document indicating awareness of the investigational nature and the risks of this study * Willingness and ability to comply with scheduled visits, treatment plan, laboratory tests, and other study procedures. Exclusion criteria: * Prior history of invasive breast carcinoma * Treatment with any other investigational agents for this condition. * Major surgical procedure (excluding placement of vascular access) or significant traumatic injury within 28 days of study entry or an anticipated need for major surgery during the study. * Extracranial palliative radiotherapy within 7 days prior to enrollment. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to trastuzumab, pertuzumab, paclitaxel, trastuzumab deruxtecan, trastuzumab emtansine, tucatinib. * Participants with a medical history of myocardial infarction within 6 months before enrollment or symptomatic CHF (NYHA Class II to IV). * Subjects must not have any of the following: * Any untreated brain lesion on screening MRI, unless approved by the Sponsor Investigator * Ongoing use of systemic corticosteroids for control of symptoms of brain metastases at a total daily dose of \>2 mg of dexamethasone (or equivalent). * Known or concurrent leptomeningeal disease on screening MRI * Poorly controlled (\>1/week) generalized or complex partial seizures * History of arrhythmia (multifocal premature ventricular contractions, bigeminy, trigeminy, ventricular tachycardia), which is symptomatic or requires treatment (CTCAE Grade 3), symptomatic or uncontrolled atrial fibrillation despite treatment, or asymptomatic sustained ventricular tachycardia. Participants with atrial fibrillation controlled by medication or arrhythmias controlled by pacemakers may be permitted upon discussion with the Sponsor-Investigator. * History of (non-infectious) ILD/pneumonitis that required steroids, has current ILD/pneumonitis, or where suspected ILD/pneumonitis cannot be ruled out by imaging at screening. * History of other lung disease, such as: * Lung-specific intercurrent clinically significant illnesses including, but not limited to, any underlying pulmonary disorder (e.g., pulmonary emboli within 3 months of study enrolment, severe asthma, severe chronic obstructive pulmonary disorder (COPD), restrictive lung disease, pleural effusion etc.). * Any autoimmune, connective tissue or inflammatory disorders (e.g., rheumatoid arthritis, Sjogren's, sarcoidosis, etc.) where there is documented, or a suspicion of pulmonary involvement at the time of screening. * Prior pneumonectomy. * Active or uncontrolled clinically serious infection * Have inability to swallow pills or significant gastrointestinal disease which would preclude the adequate oral absorption of medications * Have ongoing ≥ Grade 2 diarrhea of any etiology * Participants receiving any medications or substances that are inhibitors or inducers of CYP2C8 and/or CYP3A4 are ineligible. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently updated medical reference. * Pregnant women are excluded from this study because of potential for teratogenic or abortifacient effects of study drugs. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with study drugs, breastfeeding should be discontinued prior to enrollment.