Tucatinib, Palbociclib and Letrozole in Metastatic Hormone Receptor Positive and HER2-positive Breast Cancer

Inclusion Criteria: 1. Subjects must have a histologically confirmed diagnosis of HR+/HER2+ locally advanced unresectable or metastatic breast cancer. Estrogen or progesterone receptor positivity is defined by IHC according to the most recent ASCO/CAP guidelines. HER2 positivity is defined by standard of care fluorescence in situ hybridization (FISH) and/or 3+ staining by IHC according to the most recent ASCO/CAP guidelines. 2. Measurable and/or evaluable disease per RECIST 1.1 criteria and/or RANO-BM criteria . Bone only disease is allowed. 3. CNS inclusion criteria: * Subjects without CNS metastases are eligible. Note: brain imaging is not required for asymptomatic subjects without known brain metastatic disease prior to enrollment into the study * Subjects with untreated asymptomatic CNS metastases not needing immediate local therapy in the opinion of investigator are eligible. For subjects with untreated asymptomatic CNS lesions \> 2.0 cm by contrast-enhanced MRI, discussion with and approval from the Lead PI is required prior to enrollment * Subjects with stable brain metastases previously treated with radiation therapy or surgery are allowed to enroll, provided that they are off corticosteroids or on stable/tapering dose of corticosteroids and stability of CNS metastatic disease for at least 4 weeks has been demonstrated, with the last MRI taken within 2 weeks prior to cycle 1 day 1 of the study. Relevant records of any CNS treatment must be available to allow for classification of target and non-target lesions 4. Age ≥ 18 years 5. ECOG performance status 0-1 6. Life expectancy of more than 6 months, in the opinion of the investigator 7. Study subjects should be post-menopausal women; premenopausal women are eligible if on ovarian suppression, or agreeable to mandatory ovarian suppression. Women of childbearing potential, defined as premenopausal women who are not permanently sterile (i.e., due to hysterectomy, bilateral oophorectomy, bilateral tubal ligation, or bilateral tubal occlusion) are required to have negative pregnancy tests prior to initiation of treatment. 8. Prior treatments: * Subjects should have received at least two approved HER2-targeted agents (trastuzumab, pertuzumab, or TDM-1) in the course of their disease * Subjects should have had at least 1 line of prior HER2-targeted therapy in the metastatic setting, with the exception of asymptomatic subjects with oligometastatic or bone / soft tissue only disease who, on investigator opinion, are appropriate for a single agent antiendocrine therapy per NCCN guidelines * Subjects who have had up to 2 lines of prior endocrine therapy in the metastatic setting are allowed. Prior adjuvant and/or neoadjuvant endocrine regimens are allowed and not counted towards this limit 9. Adequate organ and marrow function as defined below: * Absolute neutrophil count ≥ 1,500/mm3 * Platelets ≥ 75,000/mm3 * Hemoglobin ≥ 9.0 mg/dL without red blood cell transfusion ≤ 7 days prior to Cycle 1Day 1 of therapy * Total serum bilirubin ≤ 1.5 X upper limit of normal (ULN) except for subjects with known Gilbert's disease, who may enroll if the conjugated bilirubin is ≤ 1.5 ULN * AST (SGOT)/ALT (SGPT) ≤2.5 X ULN; * Serum creatinine ≤ 1.5 mg/dL * International normalized ratio (INR) and activated partial thromboplastin time (aPTT) ≤1.5 X ULN unless on medication known to alter INR and aPTT * Left ventricular ejection fraction (LVEF) ≥ 50% (as assessed by ECHO or MUGA) documented within 4 weeks prior to first dose of study treatment * Serum or urine pregnancy test (for women of childbearing potential) negative ≤ 7 days of starting treatment 10. Ability to understand and the willingness to sign a written informed consent and comply with the study scheduled visits, treatment plans, laboratory tests and other procedures. 11. Subject or legally authorized representative of a subject must provide signed informed consent per a consent document that has been approved by an institutional review board or independent ethics committee (IRB/IEC) prior to initiation of any study-related tests or procedures that are not part of standard-of-care for the subject's disease. Exclusion criteria: 1. Subjects with previously treated progressing brain metastases are excluded from the study 2. Subjects with known brain metastases and contraindications to undergo contrast MRI imaging of the brain are excluded from the study 3. Pregnancy or breast feeding 4. Current active treatment with an investigational agent 5. Known history of hypersensitivity to aromatase-inhibitor drugs 6. Any toxicity related to prior cancer therapies that has not resolved to ≤ Grade 1, with the exception of peripheral neuropathy, which must have resolved to ≤ Grade 2, and alopecia 7. Previous treatment with lapatinib, neratinib, afatinib, or other investigational EGFR-family receptor tyrosine kinase inhibitor or HER2 tyrosine kinase inhibitor 8. Previous treatment with palbociclib, abemaciclib, ribociclib or other investigational CDK4/6 inhibitors 9. Any systemic anti-cancer therapy (including hormonal therapy), radiation, or experimental agent ≤ 2 weeks of first dose of study treatment 10. Active bacterial, fungal or viral infections requiring treatment with IV antibiotic, IV antifungal, or IV anti-viral drugs 11. Known hepatitis B (HBV), hepatitis C (HCV) or human immunodeficiency virus (HIV) infections. Note: pretesting is not required. 12. Inability to swallow pills or any significant gastrointestinal disease which would preclude the adequate oral absorption of medications 13. Use of prohibited medications within 3 elimination half-lives prior to first dose of the study treatment 14. Known myocardial infarction, severe/unstable angina, percutaneous transluminal coronary angioplasty/stenting (PTCA), or coronary artery bypass graft (CABG) within 6 month of the first dose of the study treatment 15. Clinically significant cardio-vascular disease, such as ventricular arrhythmia requiring therapy, uncontrolled hypertension (defined as persistent systolic blood pressure \> 160 mm Hg and/or diastolic blood pressure \> 100 mm Hg on antihypertensive medications), or any history of symptomatic congestive heart failure (CHF) 16. Other severe acute or chronic medical or psychiatric conditions or laboratory abnormalities that may increase the risk associated with study participation or study drug administration, or may interfere with the interpretation of study results, or in the judgment of the investigator would make the subject inappropriate for entry into the study.