Inclusion Criteria:

          -  Age >= 18 years old

          -  Pathologically confirmed advanced or metastatic malignancy characterized by one or
             more of the following: Subject is intolerant of standard therapy. Malignancy is
             refractory to standard therapy. Malignancy relapsed after standard therapy. Malignancy
             for which there is no standard therapy that improves survival by at least 3 months.

          -  Evaluable tumor(s) with documented alteration(s) in FGF/FGFR-related gene(s). The
             FGF/FGFR aberration(s) can be identified at any point in the subject's cancer course.
             FGF/FGFR testing must have been performed in a CLIA-certified laboratory.
             Amplification(s) and/or mutation frequenc(ies) will be defined according to the
             standard of the test used. One example, Foundation OneTM, defines amplifications as ≥
             6 copies and base substitution mutations as present if there is ≥ 5% mutant allele
             frequency.

          -  Subjects must meet the following laboratory requirements at screening (may be
             repeated): Adequate bone marrow function: absolute neutrophil count ≥ 1,500/mL;
             hemoglobin ≥ 8.5 g/dL, platelets ≥ 75,000/mL. Adequate liver function: transaminases
             (AST/ALT) and alkaline phosphatase ≤ 3 (≤ 5 X Upper Limit of Normal (ULN) in the
             setting of liver metastasis) x ULN; bilirubin ≤ 1.5 x ULN. Adequate renal function:
             creatinine clearance ≥ 40 mL/min (Cockcroft Gault). Adequate blood coagulation:
             international normalized ratio (INR) ≤ 2.3. Serum amylase and lipase ≤ 1.5 x ULN.

          -  Adequately controlled blood pressure (BP): BP ≤ 150/90 mm Hg at screening (may be
             repeated and may be controlled with anti-hypertensive medication).

          -  Adequate performance status (PS): Eastern Cooperative Oncology Group (ECOG) PS 0-2

          -  Women of childbearing potential must have a negative baseline blood pregnancy test.
             Women and men must agree to use adequate contraception (hormonal or barrier method of
             birth control; abstinence) for the duration of study and for at least 30 days after
             discontinuation of study drug (the half life of lenvatinib is about 28 hours in
             patients with cancer).

          -  Subjects must be off other anti-tumor agents for at least 5 half lives of the agent or
             4 weeks from the last day of treatment, whichever is shorter. Endocrine therapies (for
             example for breast or prostate cancer) and anti-Her2 therapies (for example,
             trastuzumab or lapatinib) are allowed to continue while on this study.

          -  Subjects may not be receiving any other experimental agents or agents that are not FDA
             approved.

          -  Ability to understand and willingness to sign a written consent document.

        Exclusion Criteria:

          -  Pregnant or lactating women.

          -  Subjects with known hypersensitivity to any of the components or metabolites of the
             drug product.

          -  Subjects with FGFR mutations known to be inactivating. Mutations of unknown
             significance (based on most currently available information) will be allowed.

          -  Subjects who have not recovered from toxicities as a result of prior anticancer
             therapy, except alopecia and infertility. Recovery is defined as < Grade 2 severity
             per Common Terminology Criteria for Adverse Events Version 4.0 (CTCAE v4.0).

          -  Significant cardiovascular impairment: history of congestive heart failure greater
             than New York Heart Association (NYHA) Class II, unstable angina, myocardial
             infarction or stroke within 6 months of the first dose of study drug, or cardiac
             arrhythmia requiring medical treatment at Screening.

          -  Inability to swallow pills or determination by the investigator that absorption of
             oral medication would be impaired.

          -  Major surgery (not including placement of central lines) within 3 weeks prior to
             randomization or planned surgery during the course of this study.

          -  Any medical condition which, in the opinion of the investigator, would preclude study
             participation.

          -  Subjects who are considered members of a vulnerable population (for example,
             prisoners).