Inclusion Criteria:

        Subjects must fulfill all of the following inclusion criteria.

          1. Able to understand and comply with study procedures, understand the risks involved in
             the study, and provide written informed consent before any study-specific procedure is
             performed.

          2. Men or women 18 years of age or older.

          3. Subjects with histologically or cytologically confirmed advanced solid tumors that are
             metastatic or unresectable, who are refractory or have relapsed after treatment with
             available therapies or for whom standard life-prolonging measures or approved
             therapies are not available. In Phase 1 Part B and in the Phase 2 portion of the
             protocol, subjects must also have documented gene alterations in the MAPK pathway as
             detailed in the protocol.

          4. In Phase 1 Part B of the protocol, subjects must have disease lesions that are
             amenable to biopsy.

          5. In the Phase 2 portion of the protocol, subjects must have measurable disease
             according to RECIST v1.1.

          6. Eastern Cooperative Oncology Group performance status 0 to 2.

          7. Acceptable organ function as evidenced by the following laboratory data:

               1. Aspartate aminotransferase (AST) and alanine aminotransferase ≤2×upper limit of
                  normal (ULN) or ≤3 ULN in the presence of liver metastases.

               2. Total serum bilirubin ≤1.5×ULN.

               3. Absolute neutrophil count (ANC) ≥1500 cells/mm3.

               4. Platelet count ≥100,000 cells/mm3.

               5. Calculated creatinine clearance (by the standard Cockcroft Gault formula) of ≥50
                  mL/min or glomerular filtration rate of ≥50 mL/min.

          8. Women of child-bearing potential (according to recommendations of the Clinical Trial
             Facilitation Group [CTFG]; see protocol for details) must not be pregnant or
             breastfeeding and must have a negative pregnancy test within 24 hours before the first
             dose of study treatment. While receiving study treatment and for at least 5 half-lives
             of ASTX029 or metabolite plus 30 days after completing treatment, women of
             child-bearing potential must agree to practice highly effective contraceptive measures
             (as described in the protocol) and must refrain from donating eggs (ova, oocytes) for
             the purpose of reproduction.

          9. Men with female partners of child-bearing potential (according to recommendations of
             the CTFG; see protocol for details) must agree to, during the treatment period and for
             at least 5 half-lives of ASTX029 or metabolite plus 90 days after completing
             treatment, practice highly effective contraceptive measures (as described in the
             protocol), not to father a child, and to refrain from donating sperm.

        Exclusion Criteria:

          1. Hypersensitivity to ASTX029 or excipients of the drug product.

          2. Poor medical risk in the investigator's opinion because of systemic diseases in
             addition to the cancer under study, for example, uncontrolled infections.

          3. Life-threatening illness, significant organ system dysfunction, or other condition
             that, in the investigator's opinion, could compromise subject safety or the integrity
             of study outcomes or interfere with the absorption or metabolism of ASTX029.

          4. Prior anticancer treatments or therapies within the indicated time window prior to
             first dose of study treatment (ASTX029), as follows:

               1. Cytotoxic chemotherapy or radiotherapy within 3 weeks prior. Palliative
                  radiotherapy to a single lesion within 2 weeks prior. Any encountered
                  treatment-related toxicities (excepting alopecia) not stabilized or resolved to
                  ≤Grade 1.

               2. Monoclonal antibodies within 4 weeks prior. Any encountered treatment-related
                  toxicities not stabilized or resolved to ≤Grade 1.

               3. Molecularly targeted drug or investigational drugs, without the potential for
                  delayed toxicity, within 4 weeks of the first dose of study treatment or 5
                  half-lives (minimum 14 days), whichever is shorter. Any encountered
                  treatment-related toxicities (excepting alopecia) not stabilized or resolved to
                  ≤Grade 1.

          5. Prior treatment with extracellular signal-regulated kinase (ERK) inhibitors.

          6. History of, or at risk for, cardiac disease, as evidenced by 1 or more of the
             following conditions:

               1. Abnormal left ventricular ejection fraction (LVEF; <50%) on echocardiogram (ECHO)
                  or multiple-gated acquisition (MUGA) scan.

               2. Congestive cardiac failure of ≥Grade 3 severity according to New York Heart
                  Association functional classification defined as patients with marked limitation
                  of activity and who are comfortable only at rest.

               3. Unstable cardiac disease including unstable angina or hypertension as defined by
                  the need for overnight hospital admission within the last 3 months (90 days).

               4. History or evidence of long QT interval corrected for heart rate (QTc),
                  ventricular arrhythmias including ventricular bigeminy, complete left bundle
                  branch block, clinically significant bradyarrhythmias such as sick sinus
                  syndrome, second- and third-degree atrioventricular (AV) block, presence of
                  cardiac pacemaker or defibrillator, or other significant arrhythmias.

               5. Screening 12-lead electrocardiogram (ECG) with measurable QTc interval of ≥470
                  msec. (Fridericia's formula should be used to calculate the QTc interval
                  throughout the study.)

          7. Known history of human immunodeficiency virus (HIV) infection or seropositive results
             consistent with active hepatitis B virus (HBV) or active hepatitis C virus (HCV)
             infection.

          8. Known brain metastases, unless previously treated and stable for at least 3 months
             with or without steroids.

          9. Known significant mental illness or other conditions, such as active alcohol or other
             substance abuse that, in the opinion of the investigator, predispose the subject to
             high risk of noncompliance with the protocol treatment or assessments.

         10. History or current evidence/risk of retinal vein occlusion (RVO) or central serous
             retinopathy (CSR) including:

               1. Presence of predisposing factors to RVO or CSR (eg, uncontrolled glaucoma or
                  ocular hypertension, uncontrolled diabetes mellitus) or

               2. Visible retinal pathology as assessed by ophthalmic examination at screening that
                  is considered a risk factor for RVO or CSR such as:

                    -  Evidence of optic disc cupping or

                    -  Evidence of new visual field defects on automated perimetry or

                    -  Intraocular pressure >21 mmHg as measured by tonography.