Inclusion Criteria:

          -  Part 1: HCC; cholangiocarcinoma; or esophageal, nasopharyngeal, or serious ovarian
             cancer, regardless of FGF19/FGFR4 status; or other solid tumor malignancies with
             documented FGF19/FGFR4 alteration (FGF19/FGFR4 pathway activating alterations include,
             but are not limited to, FGFR4 amplification, FGFR4 activating mutations, and FGF19
             amplification) based on local testing.

          -  Part 2: Subjects will be enrolled into 1 of 3 cohorts:

               -  Cohort A: HCC with FGF19 amplification.

               -  Cohort B: HCC without FGF19 amplification.

               -  Cohort C: cholangiocarcinoma, esophageal, nasopharyngeal or serous ovarian
                  cancers (regardless of FGF19/FGFR4 status), or other solid tumor malignancies
                  with documented FGF19/FGFR4 alteration.

          -  Has progressed after prior therapy and either a) there is no further effective
             standard anticancer therapy available (including subject refusal) or b) is intolerant
             to standard anticancer therapy.

          -  Life expectancy > 12 weeks.

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 (Part 1) or 0-2
             (Part 2).

          -  Archival tumor specimen according to protocol-defined criteria.

          -  Centrally analyzed screening C4 (bile acid synthesis precursor) results must be below
             40.9 ng/mL, which is the upper limit as determined by the sponsor.

          -  Must agree to take bile acid sequestrants while taking INCB062079.

        Exclusion Criteria:

          -  Treatment with other investigational study drug for any indication for any reason, or
             receipt of anticancer medications within 28 days before first dose of study drug;
             subjects must have recovered from AEs due to previously administered therapies.

          -  Prior receipt of a selective FGFR4 inhibitor within the last 6 months.

          -  Laboratory parameters outside the protocol-defined ranges.

          -  History or presence of an abnormal ECG that in the investigator's opinion is
             clinically meaningful.

          -  Prior radiotherapy within 2 weeks of study treatment. A 1-week washout period is
             permitted for palliative radiation to non- central nervous system (CNS) disease with
             medical monitor approval.

          -  History of human immunodeficiency virus infection.

          -  Untreated brain or CNS metastases or brain/CNS metastases that have progressed.
             Subjects with previously treated and clinically stable brain/CNS metastases and who
             are off all corticosteroids for ≥ 4 weeks are eligible.

          -  Chronic or current active infectious disease requiring systemic antibiotic,
             antifungal, or antiviral treatment, except concomitant antiviral systemic therapy for
             chronic hepatitis B or C.

          -  Child-Pugh liver function Class B or C.

          -  History of clinically significant or uncontrolled cardiac disease.

          -  History of allergic reactions to INCB062079, any of the excipients of INCB062079 or
             similar compounds.

          -  Pregnant or nursing women or subjects expecting to conceive or father children within
             the projected duration of the study, starting with the screening visit through 90 days
             after last dose of study drug.

          -  Any medical condition that would in the investigator's judgment interfere with full
             participation in the study, including administration of study medication and attending
             required study visits; pose a significant risk to the subject; or interfere with
             interpretation of study data.