Inclusion Criteria:

          1. 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:

             A. Cohort 1 i. 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.

             ii. Measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST)
             Version 1.1 iii. Has received 1-3 prior endocrine-containing therapies and up to 2
             prior chemotherapy regimens for advanced/metastatic disease iv. Has received prior
             treatment with a CDK4/6 inhibitor or is ineligible for such i. treatment (per
             Investigator decision) ii. Has experienced disease progression/recurrence within 1
             month following the completion of any endocrine therapy for advanced/metastatic breast
             cancer

             B. Cohort 2 i. 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.

             ii. Measurable disease per RECIST 1.1 iii. Has received at least 1 prior chemotherapy
             or chemotherapy/immunotherapy iv. (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

             C. Cohort 3 i. TNBC or HR+ HER2- breast cancer (defined as above) harboring an FGFR2
             gene amplification ii. Non measurable, evaluable disease per RECIST 1.1. Patients with
             bone-only disease must have lytic or mixed lytic-blastic lesions iii. Other criteria
             for either HR+ HER2- breast cancer or TNBC should be met as described for Cohort 1 and
             2, respectively

             D. Cohort 4 i. HR+ HER2- breast cancer (defined as above) harboring an FGFR1
             high-level gene amplification ii. Measurable disease per RECIST 1.1 iii. 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.

             iv. Has received prior treatment with a CDK4/6 inhibitor or is ineligible for such i.
             treatment (per Investigator decision) ii. 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.

             iii. Has experienced disease progression/recurrence within 1 month following the
             completion of any endocrine therapy for advanced/metastatic breast cancer.

          2. Archival or (preferably) fresh tumor tissue must be available for central laboratory
             confirmation of FGFR amplification.

          3. The patient has adequate organ function as defined by the following criteria:

               1. 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

               2. Total bilirubin ≤1.5 × ULN or ≤3 × ULN in case of Gilbert's syndrome

               3. Absolute neutrophil count (ANC) ≥1.0 × 109/L without hematopoietic growth factor
                  support

               4. Platelet count ≥75 × 109/L without transfusion support (that is, excluding
                  measurements obtained within 3 days after transfusion of platelets)

               5. 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)

               6. Serum phosphorus ≤ ULN

               7. 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:

          1. History and/or current evidence of any of the following disorders:

               1. Non-tumor related alteration of the calcium-phosphorus homeostasis that is
                  considered clinically significant in the opinion of the Investigator

               2. 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

               3. Retinal or corneal disorder confirmed by retinal/corneal examination and
                  considered clinically significant in the opinion of the Investigator.

          2. 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.

          3. Treatment with any of the following within the specified time frame prior to the first
             dose of TAS-120:

               1. Major surgery within 4 weeks (the surgical incision should be fully healed)

               2. Radiotherapy for extended field within 4 weeks or limited field radiotherapy
                  within 2 weeks

               3. Any prior systemic therapy regardless of the stop date, but the patient must have
                  recovered to eligibility levels from prior toxicity

               4. Any investigational agent received within 30 days or 5 half-lives (whichever is
                  shorter)

          4. Prior treatment with an FGFR inhibitor

          5. Cohort 4 only: Prior treatment with fulvestrant, or known hypersensitivity to
             fulvestrant.

          6. A serious illness or medical condition(s) including but not limited to the following:

               1. Known acute systemic infection

               2. Myocardial infarction, severe/unstable angina, or symptomatic congestive heart
                  failure within the previous 6 months

               3. History or current evidence of serious uncontrolled ventricular arrhythmia

               4. Chronic diarrhea diseases considered to be clinically significant in the opinion
                  of the Investigator

               5. Congenital long QT syndrome, or any known history of torsade de pointes, or
                  family history of unexplained sudden death

               6. 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

          7. Brain metastases that are untreated or clinically or radiologically unstable (that is,
             have been stable for <1 month)

          8. History of another primary malignancy that is currently clinically significant or
             currently requires active intervention

          9. Pregnant or lactating female