Fulvestrant, Palbociclib and Erdafitinib in ER+/HER2-/FGFR-amplified Metastatic Breast Cancer

Inclusion Criteria: * Patients must be able to swallow and retain oral medication * Patients must be ≥ 18 years of age * Female patients of no childbearing potential must be post-menopausal. Postmenopausal female subjects should be defined prior to protocol enrollment by any of the following: * Participants at least 60 years of age; OR * Participants under 60 years of age and naturally (spontaneous, no alternative pathologic or physiological cause) amenorrhea for at least 12 months; OR * Medical ovarian failure confirmed by follicle-stimulating hormone (FSH) and estradiol levels in the post menopausal range per local institutional normal range; OR * Prior bilateral oophorectomy; OR * Prior radiation castration with amenorrhea for at least 6 months; OR * Treatment with a luteinizing hormone-releasing hormone (LH-RH) agonist (such as goserelin acetate or leuprolide acetate) is permitted for induction of ovarian suppression as long as it has been initiated at least 28 days prior to study enrollment * Patients must have ECOG performance status 0 - 1 * Patients must have clinical stage IV or inoperable locoregional recurrent invasive mammary carcinoma that is: * ER+ and/or PgR+ (≥ 1% positive stained cells) by immunohistochemistry (IHC) * HER2-negative (by IHC or FISH, per ASCO guidelines) * FGFR1 - 4 amplified * Patients must have evaluable (may have either measurable or non-measurable) disease * Patients must have available tissue for FGFR determination * Patients must have had at least one line of therapy in the metastatic setting * Current use of any of the drugs listed on the Cautionary Concomitant Med list has to be approved by the Study Chair * Patients must have adequate hematologic, hepatic and renal function. All laboratory tests must be obtained within 2 weeks from study drug initiation. These include: * ANC ≥ 1,500/mm3 * Platelet count ≥ 100,000/mm3 * HgB ≥ 9.0 g/dL * Creatinine clearance ≥ 40 mL/min/1.73 m2 * SGOT, SGPT ≤ 2.5 x ULN if no liver metastasis present; SGOT, SGPT ≤ 4 x ULN if liver metastasis present * Albumin ≥ 2.0 g/dL * Total serum bilirubin ≤ 1.5 x ULN (≤ 3 x ULN or direct bilirubin ≤ 1.5 x ULN if known Gilbert's syndrome) * Potassium within institutional normal limits * Phosphorus ≤ institutional upper limit of normal Exclusion Criteria: * Prior use of an FGFR inhibitor * More than 2 lines of chemotherapy in the metastatic setting. No limit on endocrine therapy lines. Prior exposure to CDK4/6 inhibitor acceptable. * Radiation therapy ≤ 2 weeks prior to study entry. Patients who have received prior radiotherapy must have recovered from toxicity (≤ grade 1) induced by this treatment (except for alopecia) * Prior cancer therapy (except for endocrine therapy) must have been discontinued for 1 week prior to initiation of study drugs * Concurrent anti-cancer therapy other than the ones specified in the protocol is not permitted during study participation. Bisphosphonates or denosumab are allowed * Major surgery within 4 weeks of enrollment * Herbal preparations are not allowed throughout the study, and should be discontinued 14 days prior to initiation of study treatment * Any corneal or retinal abnormality likely to increase the risk of eye toxicity, such as: * Current corneal pathology such as keratitis, keratoconjunctivitis, keratopathy, corneal abrasion, inflammation or ulceration * Uncontrolled glaucoma despite standard of care therapy * Diabetic retinopathy with macular edema * Known active wet, age-related macular degeneration (AMD) * Known central serous retinopathy (CSR) or retinal vascular occlusion (RVO) * Uncontrolled intercurrent illness including, but not limited to: * Malabsorption syndrome significantly affecting gastrointestinal function * Ongoing or active infection requiring antibiotics/antivirals * Impairment of lung function (COPD \> grade 2, lung conditions requiring oxygen therapy) * Symptomatic congestive heart failure * Unstable angina pectoris, angioplasty, stenting, or myocardial infarction within 6 months * Clinically significant cardiac arrhythmia (multifocal premature ventricular contractions, bigeminy, trigeminy, ventricular tachycardia that is symptomatic or requires treatment \[National Cancer Institute -Common Terminology Criteria for Adverse Events, Version 4.03, grade 3\] * QTcF ≥ 480 msec on screening EKG * Known history of clinically significant QT/QTc prolongation or Torsades de Pointes(TdP) * ST depression or elevation of ≥ 1.5 mm in 2 or more leads * Diarrhea of any cause ≥ CTCAE grade 2 that does not resolve within a few days when adequately treated with anti-diarrhea medications * Psychiatric illness/social situations that would compromise patient safety or limit compliance with study requirements including maintenance of a compliance/pill diary * Symptomatic brain metastases (patients with a history of brain metastases must be clinically stable for more than 4 weeks from completion of radiation treatment and be off steroids) * Known history of chronic liver or chronic renal failure * Poor wound healing capacity