Inclusion Criteria:

          -  written informed consent obtained prior to any study-related procedures.

          -  Eastern Cooperative Oncology Group Performance Status: 0-1

          -  Part A only: Histologically or cytologically confirmed metastatic and/or advanced
             solid tumors with documented progressive disease for whom no further standard therapy
             is indicated.

          -  Part B only: 5. Histologically or cytologically confirmed, molecularly selected (i.e.
             BRAFV600 positive and/or PI3K mutation positive) advanced solid tumors. Prior
             molecular characterization should be based using a regulatory approved assay or
             analytically validated assay.

               -  Group 1: BRAFV600 positive metastatic or recurrent melanoma after failure of
                  prior treatment with standard therapy such as a checkpoint inhibitor and an
                  approved B-RAF inhibitor (vemurafenib or dabrafenib)

               -  Group 2: BRAFV600 positive metastatic colorectal carcinoma (CRC), or advanced
                  non-small cell lung carcinoma (NSCLC) after failure of at least two lines of
                  prior standard therapy or for whom no further standard therapy is indicated.

               -  Group 3: Advanced solid tumors with PI3K pathway alterations (PIK3CA mutation or
                  PTEN loss) after failure of at least one line of prior standard therapy or for
                  whom no further standard therapy is indicated. Prior treatment may not include
                  inhibitors of the PI3K pathway.

          -  Screening hematology values of the following: absolute neutrophil count ≥ 1000/μL,
             platelets ≥ 100,000/μL, hemoglobin ≥ 10 g/dL (without transfusion support);

          -  Screening chemistry values of the following: alanine aminotransferase (ALT) and
             aspartate transaminase (AST) ≤ 3.0 × upper limit of the normal reference range (ULN),
             total bilirubin ≤ 2 × ULN, creatinine ≤ 1.5 × ULN, fasting blood glucose < 140 mg/dL,
             hemoglobin A1C ≤ ULN, albumin ≥ 2.8 g/dL.

          -  Screening fasting lipid panel: LDL cholesterol < 190 mg/dL, triglycerides < 300 mg/dL

          -  Subject is willing and able to comply with all protocol required visits and
             assessments, including biopsy if assigned to the MTD expansion cohort;

        Exclusion Criteria:

          -  Have received prior chemotherapy, other investigational therapy, or major surgery
             within 4 weeks of Day 1;

          -  Have received oral anti-cancer therapy with oral tyrosine kinase inhibitors within 14
             days or 5 half-lives, whichever is longer.

          -  Have received prior treatment with monoclonal antibodies within 6 weeks of first dose
             of Day 1;

          -  Subject has received a live virus vaccine within the previous 8 weeks.

          -  Have known central nervous system metastasis or primary tumor (Part A).
             Previously-treated, CNS metastasis is permitted in Part B. CNS metastasis must be
             small, discrete metastasis; stable for at least 30 days without the need for
             concomitant prednisone for symptom management. No leptomeningeal disease is allowed.
             Is receiving therapeutic doses of corticosteroids (>20 mg prednisone daily or
             equivalent);

          -  Has a serious concurrent medical condition such as:

               -  history of Diabetes Mellitus, type 1 or type 2,

               -  known autoimmune disease, known bleeding diathesis, history of congestive heart
                  failure New York Heart Association (NYHA) class III or IV;

               -  uncontrolled hypertension (systolic BP ≥ 139 mmHg or diastolic BP ≥ 89 mmHg) at
                  screening, despite optimal antihypertensive therapy,

               -  clinically significant heart disease including but not limited to: myocardial
                  infarction, or arterial thrombotic events in the past 6 months, severe or
                  unstable angina, or known cardiac ejection fraction measurement of < 50 %;

               -  history or family history of long QT syndrome; 12-Lead electrocardiogram (ECG)
                  abnormalities considered by the investigator to be clinically significant or QTcF
                  ≥ 450 milliseconds, regardless of clinical significance, at screening. Abnormal
                  ECG may be confirmed with one repeat assessment. For subjects with QTcF ≥ 450
                  msec on initial ECG, the mean of the two QTcF assessments will determine
                  eligibility;

               -  uncontrolled psychiatric illness;

               -  serious persistent infection within 14 days prior to the start of study
                  medication;

               -  known gastrointestinal disease or condition which may affect the absorption of
                  ASN003;

               -  known active or symptomatic viral hepatitis, chronic liver disease or liver
                  cirrhosis;

               -  known glaucoma or other pre-existing ocular conditions that may put the patient
                  at risk for ocular toxicities.

               -  any known condition or situation which may put the patient at significant risk,
                  may confound the study results, or may interfere significantly with subject's
                  participation in the study

          -  Female subjects who are pregnant or breast feeding