Inclusion Criteria:

• Histologically or cytologically confirmed recurrent locally advanced or metastatic breast cancer not amenable to treatment with curative intent, meeting all of the criteria for 1 of the following cohorts:

Cohort 1

• HR+ HER2- breast cancer harboring an FGFR2 gene amplification. HR+ HER2- breast cancer is defined per the local pathology report as estrogen receptor (ER) >1% and/or progesterone receptor (PR) >1%, HER2-negative per American Society of Clinical Oncology (ASCO) and the College of American Pathologists (CAP) guidelines, 2018,
• Measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) Version 1.1,
• Has received 1-3 prior endocrine-containing therapies and up to 2 prior chemotherapy regimens for advanced/metastatic disease;
• Has received prior treatment with a CDK4/6 inhibitor or is ineligible for such: 
  • Treatment (per Investigator decision); 
  • Has experienced disease progression/recurrence within 1 month following the completion of any endocrine therapy for advanced/metastatic breast cancer.

Cohort 2

• TNBC harboring an FGFR2 gene amplification. TNBC is defined as negative for ER, PR and HER2. Negative for ER and PR includes the following:
  • Local pathology report classifies them as negative, Allred Score of 2 or below or <1% staining. HER2-negative per ASCO / CAP guidelines, 2018;
  • Measurable disease per RECIST 1.1;
  • Has received at least 1 prior chemotherapy or chemotherapy/immunotherapy;
  • (PD-L1/PD-1 inhibitors) regimen for advanced/metastatic disease;
  • Has experienced disease progression/recurrence during or after the most recent prior chemotherapy for advanced/metastatic breast cancer.

Cohort 3

• TNBC or HR+ HER2- breast cancer (defined as above) harboring an FGFR2 gene amplification.
• Non measurable, evaluable disease per RECIST 1.1. Patients with bone-only disease must have lytic or mixed lytic-blastic lesions.
• Other criteria for either HR+ HER2- breast cancer or TNBC should be met as described for Cohort 1 and 2, respectively.

Cohort 4

• HR+ HER2- breast cancer (defined as above) harboring an FGFR1 high-level gene amplification.
• Measurable disease per RECIST 1.1.
• Has received 1-2 prior endocrine-containing therapies and no more than 1 prior chemotherapy regimen for advanced/metastatic disease. Prior treatment with fulvestrant is not permitted.
• Has received prior treatment with a CDK4/6 inhibitor or is ineligible for such: 
  • Treatment (per Investigator decision);
  • Pre/peri-menopausal patients must be on goserelin. Patients must have commenced treatment with goserelin or an alternative GnRH agonist at least 4 weeks prior to the first dose of fulvestrant. If patients have received an alternative GnRH agonist prior to study entry, they must switch to goserelin for the duration of the trial. Postmenopausal is defined as at least one of the following criteria: age ≥60 years; age <60 years and cessation of regular menses for at least 12 consecutive months with no alternative pathological or physiological cause; and serum estradiol and follicle-stimulating hormone level within the laboratory's reference range for postmenopausal females; or documented bilateral oophorectomy;
  • Has experienced disease progression/recurrence within 1 month following the completion of any endocrine therapy for advanced/metastatic breast cancer.
• Archival or (preferably) fresh tumor tissue must be available for central laboratory confirmation of FGFR amplification.
• The patient has adequate organ function as defined by the following criteria:
  • Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3.0 × the upper limit of normal (ULN); if liver function abnormalities are due to underlying liver metastases, AST and ALT ≤ 5 × ULN;
  • Total bilirubin ≤ 1.5 × ULN or ≤ 3 × ULN in case of Gilbert's syndrome;
  • Absolute neutrophil count (ANC) ≥ 1.0 × 10^9/L without hematopoietic growth factor support;
  • Platelet count ≥ 75 × 10^9/L without transfusion support (that is, excluding measurements obtained within 3 days after transfusion of platelets);
  • Hemoglobin ≥ 9.0 g/dL without transfusion support (that is, excluding measurements within 7 days after transfusion of packed red blood cells or whole blood);
  • Serum phosphorus ≤ ULN;
  • Creatinine clearance (calculated or measured value): ≥ 40 mL/min.

Exclusion Criteria:

A patient must not meet any of the following exclusion criteria to be eligible for this study:

• History and/or current evidence of any of the following disorders:
  • Non-tumor related alteration of the calcium-phosphorus homeostasis that is considered clinically significant in the opinion of the Investigator;
  • Ectopic mineralization/calcification, including but not limited to soft tissue, kidneys, intestine, or myocardia and lung, considered clinically significant in the opinion of the Investigator;
  • Retinal or corneal disorder confirmed by retinal/corneal examination and considered clinically significant in the opinion of the Investigator;
  • Corrected QT interval using Fridericia's formula (QTcF) > 470 msec. Patients with an atrioventricular pacemaker or other condition (for example, right bundle branch block) that renders the QT measurement invalid are an exception and the criterion does not apply.
• Treatment with any of the following within the specified time frame prior to the first dose of TAS-120:
  • Major surgery within 4 weeks (the surgical incision should be fully healed);
  • Radiotherapy for extended field within 4 weeks or limited field radiotherapy within 2 weeks;
  • Any prior systemic therapy regardless of the stop date, but the patient must have recovered to eligibility levels from prior toxicity;
  • Any investigational agent received within 30 days or 5 half-lives (whichever is shorter);
  • Prior treatment with an FGFR inhibitor.

Cohort 4 only

• Prior treatment with fulvestrant, or known hypersensitivity to fulvestrant.
• A serious illness or medical condition(s) including but not limited to the following:
  • Known acute systemic infection;
  • Myocardial infarction, severe/unstable angina, or symptomatic congestive heart failure within the previous 6 months;
  • History or current evidence of serious uncontrolled ventricular arrhythmia;
  • Chronic diarrhea diseases considered to be clinically significant in the opinion of the Investigator;
  • Congenital long QT syndrome, or any known history of torsade de pointes, or family history of unexplained sudden death;
  • Other severe acute or chronic medical or psychiatric condition or laboratory abnormality that may increase the risk associated with study participation or TAS-120 administration, or may interfere with the interpretation of study results, and in the judgment of the Investigator would make the patient inappropriate for entry into this study;
  • Brain metastases that are untreated or clinically or radiologically unstable (that is, have been stable for <1 month);
  • History of another primary malignancy that is currently clinically significant or currently requires active intervention.
• Pregnant or lactating female