Inclusion Criteria:  Adult (≥ 18 years of age). Histologically or cytologically confirmed stage IV (metastatic) breast cancer. PI approval is needed for patients who do not have source documentation of histologically confirmed stage IV (metastatic) breast cancer, but otherwise have known metastatic breast cancer. Participants must have biopsy proven HR+, i.e ER positive (ER+) and/or PR positive (PR+), HER2 non-amplified (negative), invasive breast cancer. ER, PR, and HER2 positivity would be determined per institutional (local) testing, with HR+/HER2 nonamplified (negative) status for this trial determined as per 2020 ASCO/CAP guidelines, in a biopsy/surgical specimen analyzed for ER/PR/HER2. Patients with "ER or PR low positive" (<10%) as per updated ASCO/CAP 2020 guidelines can be considered.Confirmation of adequate (15-20 unstained slides cut at 5-10 μm or 1 block) archival tissue (primary or metastatic) required before study entry. If adequate tissue not available, PI approval is required prior to study entry. Previously treated with no more than three prior chemotherapy regimens (no limit on prior endocrine-based regimens (including CDK4/6i and PI3K pathway inhibitors) or immunotherapy). In patients with disease recurrence during/within 12 months of (neo)adjuvant therapy, the (neo)adjuvant therapy would count as one prior regimen for this criterion. Radiation therapy or local therapy/surgery would not count as prior regimen for this criterion. Patient who discontinued chemotherapy during/after only one cycle and/or due to adverse effects without disease progression would not count the treatment/regimen as prior regimen for this criterion. Antibody drug conjugate and PARP inhibitor treatment would count as chemotherapy regimen for this criterion. Hyperactive HER2 signaling activity based on results from the CELsignia test (separate pre-screening test).  Postmenopausal women with locally advanced or metastatic BC. Patients must be postmenopausal women as defined by one of the following:  Women > 60 years OR  Women ≤ 60 years, and any one of the following:  LH and FSH level in the postmenopausal range according to institutional standards s/p post bilateral surgical oophorectomy Premenopausal/perimenopausal women on gonadotropin-releasing hormone agonist (to be continued during study) and estradiol level in the postmenopausal range according to institutional standards. ECOG performance status = 0-2 Measurable disease as per RECIST Version 1.1. Ability to understand and the willingness to undergo tissue biopsy for HER2 testing (CELsignia test). Patient has signed the Informed Consent (ICF) prior to any screening procedures being performed and is able to comply with protocol requirements. At least 2 weeks beyond treatment (chemotherapy, targeted therapy, immunotherapy, and/or radiation therapy) or major surgery and recovered from all acute toxicities prior to randomization. (adverse events from prior anti-cancer agents need to be grade 1 or lower; grade 2 alopecia or peripheral neuropathy is permitted).  Patient has adequate bone marrow and organ function as defined by the following laboratory values at screening:  Absolute neutrophil count ≥ 1.5 × 109/L Platelets ≥ 75 × 109/L Hemoglobin ≥ 9.0 g/dL (transfusion permitted) INR ≤1.5 GFR or creatinine clearance ≥50 mL/min (either permitted) In the absence of liver metastases, alanine aminotransferase (ALT) and aspartate aminotransferase (AST) <2.5 x ULN. If the patient has liver metastases, ALT and AST <5 x ULN. Total bilirubin ≤1.5.0 x ULN, or direct bilirubin ≤3 x ULN in patients with well documented Gilbert's Syndrome.  Exclusion Criteria:  Participants who have received prior neratinib or any anti-HER2 therapy for metastatic disease will not be eligible. Participants who have received prior fulvestrant (or any other endocrine therapy) will be eligible. Patients with known HER2 activating mutations (either plasma and/or tissue-based genotyping) will not be eligible. Participants with increasing/progressive CNS metastatic disease. Patients with asymptomatic or stable CNS metastasis are eligible, provided metastasis radiologically non-progressing for at least two weeks, and patient is not actively taking steroids (more than 20 mg of prednisone or equivalent dose). Uncontrolled inter-current illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. Patient has impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of the study drugs (e.g., ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection).  Clinically significant, uncontrolled heart disease and/or cardiac repolarization abnormality including any of the following:  History of angina pectoris, symptomatic pericarditis, coronary artery bypass graft (CABG) or myocardial infarction within 6 months prior to study entry. Known LVEF <50% (by ECHO or MUGA) and/or known documented cardiomyopathy.  History of cardiac failure, significant/symptomatic bradycardia, Long QT syndrome, family history of idiopathic sudden death or congenital long QT syndrome or any of the following:  Known risk to prolong the QT interval or induce Torsade's de Pointes. On screening, QTcF >470 screening ECG. HIV-positive participants on combination antiretroviral therapy are ineligible. These participants are at increased risk of lethal infections when treated with marrow suppressive therapy. Appropriate studies will be undertaken in participants receiving combination antiretroviral therapy when indicated. Pregnant women are excluded from this study because the safety of study medications is not established in pregnant women.  Women of child-bearing potential, defined as all women physiologically capable of becoming pregnant, or fertile men, unless they are using highly effective methods of contraception throughout the study and after study drug discontinuation (till seven months in women and four months in males, post-study). Male patient should not donate sperm while on treatment and up to 6 months after last dose. Women are considered postmenopausal and not of childbearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g. age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks ago. In the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of childbearing potential. Highly effective contraception methods include:  Total abstinence when this is in line with the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, postovulation methods) and withdrawal are not acceptable methods of contraception. Female sterilization (have had surgical bilateral oophorectomy with or without hysterectomy), total hysterectomy, or tubal ligation at least six weeks before taking study treatment. In case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment Use of oral, injected or implanted hormonal methods of contraception or placement of an intrauterine device (IUD) or intrauterine system (IUS), or other forms of hormonal contraception that have comparable efficacy (failure rate <1%), for example hormone vaginal ring or transdermal hormone contraception. In case of use of oral contraception, women should have been stable on the same pill for a minimum of 3 months before taking study treatment. Note: While oral contraceptives are allowed, they should be used in conjunction with a barrier method of contraception due to unknown effect of drug-drug interaction.