HERizon-Breast: A ctDNA-Guided Adaptive Study of Sequential Anti-HER2 Therapies and CNS Prophylaxis to Induce Long-Term Remission

Inclusion Criteria: * Male or female participants who are ≥18 years old with histologically confirmed diagnosis of unresectable locally advanced or MBC. * Stage IV at the diagnosis (i.e., de novo metastatic) as per AJCC 8. * HER2 IHC results of 3+. * Life expectancy of ≥12 weeks. * Must be deemed medically fit for surgery and be surgical candidates upfront, or potentially operable if there is response to induction therapy. * Must have measurable disease per PERCIST 1.0. * The participant (or legally acceptable representative if applicable) provides written informed consent for the trial. * Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. * Have adequate organ function as defined in the following table (Table 1). Specimens must be collected within 14 days prior to the start of study intervention. * A female participant is eligible to participate if she is not pregnant or breastfeeding, and at least one of the following conditions applies: * Is not a woman of childbearing potential (WOCBP) OR Is a WOCBP and using a contraceptive method that is highly effective (with a failure rate of \<1% per year), with low user dependency, or be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long term and persistent basis), as described in Appendix 3 during the intervention period. The investigator should evaluate the potential for contraceptive method failure (i.e., noncompliance, recently initiated) in relationship to the first dose of study intervention. * A WOCBP must have a negative urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of beta-human chorionic gonadotropin \[β-hCG\]) within 72 hours before the first dose of study intervention. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * Additional requirements for pregnancy testing during and after study intervention are located in Appendix 2.The investigator is responsible for review of medical history, menstrual history, and recent sexual activity to decrease the risk for inclusion of a woman with an early undetected pregnancy. * Male participants are eligible to participate if they agree to the following during the intervention period and for at least 7 days after the last dose of therapy. * Be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long term and persistent basis) and agree to remain abstinent OR must agree to use contraception unless confirmed to be azoospermic (vasectomized or secondary to medical cause) as detailed below: * Agree to use a male condom plus partner use of an additional contraceptive method when having penile-vaginal intercourse with a WOCBP who is not currently pregnant. Note: Men with a pregnant or breastfeeding partner must agree to remain abstinent from penile-vaginal intercourse or use a male condom during each episode of penile-vaginal penetration. * Criteria for known Hepatitis B and C positive subjects: Hepatitis B and C screening tests are required as per MSK policy but do not need to be repeated prior to study unless there is a known history of Hepatitis B Virus (HBV) or Hepatitis C Virus (HCV) infection. * Participants who have active hepatitis B infection (defined as HBsAg positive and/or detectable HBV DNA) are eligible if they have received HBV antiviral therapy for at least 4 weeks and have undetectable HBV viral load prior to randomization. Participants should remain on anti-viral therapy throughout study intervention and follow MSK guidelines for HBV anti-viral therapy post completion of study intervention. * Participants with a history of HCV infection (defined as anti-HCV Ab positive and detectable HCV RNA) are eligible if HCV viral load is undetectable at screening. * Participants must have completed curative anti-viral therapy at least 4 weeks prior to randomization. Table 1 Adequate Organ Function Laboratory Values Hematological Absolute neutrophil count (ANC): ≥1500/µL Platelets: ≥100 000/µL Hemoglobin: ≥9.0 g/dL or ≥5.6 mmol/L Renal Creatinine OR Measured or calculated creatinine clearance (GFR can also be used in place of creatinine or CrCl): ≤1.5 × ULN OR ≥30 mL/min for participant with creatinine levels \>1.5 × ULN Hepatic Total bilirubin: ≤1.5 × ULN OR direct bilirubin ≤ULN for participants with total bilirubin levels \>1.5 × ULN AST (SGOT) and ALT (SGPT) Coagulation International normalized ratio (INR) OR prothrombin time (PT) Activated partial thromboplastin time (aPTT): ≤1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants ALT (SGPT)=alanine aminotransferase (serum glutamic pyruvic transaminase); AST (SGOT)=aspartate aminotransferase (serum glutamic oxaloacetic transaminase); GFR=glomerular filtration rate; ULN=upper limit of normal. a Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within last 2 weeks. b Creatinine clearance (CrCl) should be calculated per institutional standard. Note: This table includes eligibility-defining laboratory value requirements for treatment; laboratory value requirements should be adapted according to local regulations and guidelines for the administration of specific chemotherapies. Exclusion Criteria: * Patients diagnosed with HER2+ breast cancer as per American Society of Clinical Oncology (ASCO)/College of American Pathologists (CAP) guidelines with HER2 IHC results of 1-2+ and positive FISH or ISH * Prior exposure to anti-HER2 therapy of any kind or any systemic anti-cancer treatment of any kind for breast cancer. * Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 2 weeks prior to the first dose of study intervention. * Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in doses \>10 mg daily of oral prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug. Inhaled, intranasal, intra-articular, or topical steroid use are allowed. * Has a known additional malignancy that is progressing or has required active treatment within the past 3 years. Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin or carcinoma in situ, excluding carcinoma in situ of the bladder, which have undergone potentially curative therapy are not excluded. * Has known CNS metastases and/or leptomeningeal carcinomatosis. * Has a history or evidence of active pneumonitis or interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease. * Has grade \>=3 neuropathy of any etiology. * Has an active infection requiring antibiotics. * Has a known history of Human Immunodeficiency Virus (HIV) infection. * Has an inability to swallow capsules or tablets. * Has a history or current evidence of any condition, therapy, or laboratory abnormality or other circumstance that might confound the results of the study, interfere with the participant's participation for the full duration of the study, such that it is not in the best interest of the participant to participate, in the opinion of the treating investigator. * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * Is pregnant or breastfeeding or expecting to conceive within the projected duration of the study, starting with the screening visit through 120 days after the last dose of trial treatment. * Has had an allogenic tissue/solid organ transplant. * Has significant cardiovascular impairment within 12 months of the first dose of study drug: such as NYHA Class III or IV congestive heart failure, unstable angina, myocardial infarction, cerebral vascular accident, or cardiac arrhythmia associated with hemodynamic instability. Note: Medically controlled arrhythmia would be permitted. * Has a left ventricular ejection fraction (LVEF) below the institutional normal range of 50%, as determined by multigated acquisition (MUGA) or echocardiogram (ECHO). * Known intolerance to any of the study drugs (or any of the excipients). * Has had major surgery within 3 weeks prior to first dose of study interventions. Note: Adequate wound healing after major surgery must be assessed clinically, independent of time elapsed for eligibility.