Inclusion Criteria:

          1. Life expectancy >12 weeks.

          2. BMI is between 18 to 32 kg/m2

          3. Subjects whose advanced cancer has failed treatment or whose cancer has progressed
             following available standard therapy or for whom such therapy is not acceptable to the
             subject. Subjects whose tumor tissue local laboratory results are HER2 ISH positive or
             IHC3+ must have been previously treated with a HER2 targeting therapy (e.g.
             trastuzumab, in the country or region where such therapies are available and part of
             standard of care), or have failed SOC therapy. Subjects who have been previously
             treated with a HER2 targeting therapy such as trastuzumab or ado-trastuzumab emtansine
             are eligible.

          4. Disease measurability: Phase 1a: measureable or non-measureable disease; Phase 1b:
             disease must be measureable (per RECIST v1.1) (subjects with non-measureable disease
             are not eligible for Phase 1b).

          5. Histopathologic evidence of breast cancer based upon pathologist's report.

          6. Tumor tissue local laboratory HER2 testing results (clinical pathology report) based
             on FDA or other regulatory agency approved, validated or commercially available IHC or
             ISH HER2 assay. Pre-screening for HER2 is allowed only for subjects with breast and
             gastric cancer, where applicable. Subjects with other types of cancer must have
             previously tested for HER2 status by HER2 IHC or ISH assay. 1) Phase 1a: ISH positive
             or IHC 2+ or 3+. 2) Phase 1b: Cohort 1: advanced breast cancer, ISH positive or IHC
             3+; Cohort 2: advanced breast cancer, ISH negative with IHC 2+; and Cohort 3: advanced
             gastric cancer, ISH positive or IHC 3+.

          7. Local pathology laboratory determination of HER2 status will be accepted, provided
             that the local laboratory is an accredited site for HER2 testing. In Phase 1b, if the
             local laboratory was not accredited at the time of testing, an adequate tumor tissue
             sample is required for central pathology laboratory HER2 testing. The tissue sample
             may be provided as 10 pre-cut unstained slides or a tumor block.

          8. Eastern Cooperative Oncology Group Performance Status of 0 to 1.

          9. Acute toxicities from any prior therapy, surgery, or radiotherapy must have resolved
             to Grade 0 or 1 as per the NCI-CTCAE v 4.03.

         10. The last dose of prior anticancer therapy must have been administered at least 28 days
             prior to the first dose of the IMP.

         11. Adequate bone marrow function defined by absolute neutrophil count of ≥1.5×109/L,
             platelet count of ≥100.0×109/L, and hemoglobin of ≥9.0 g/dL.

         12. Adequate hepatic function defined by serum total bilirubin ≤1.5 × upper limit of
             normal (ULN), aspartate aminotransferase/alanine aminotransferase ≤2.5 × ULN (or ≤5 ×
             ULN in subjects with liver metastases).

         13. Adequate renal function assessed by serum creatinine within reference lab normal
             limits and creatinine clearance (by Chronic Kidney Disease Epidemiology [CKD-EPI]
             Collaboration equation) ≥60 mL/min.

         14. Adequate cardiac function as assessed by cardiac troponin I within normal range; left
             ventricular ejection fraction ≥ 50% or institutional lower limit of normal; cumulative
             anthracycline dose <360 mg/m2 doxorubicin or equivalent.

         15. Willing and able to understand and sign an informed consent inform and to comply with
             all aspects of the protocol.

         16. Female subjects must be surgically sterile, or have a monogamous partner who is
             surgically sterile, or at least 2 years postmenopausal, or who commits to use an
             acceptable form of birth control (defined as the use of an intrauterine device, a
             barrier method with spermicide, condoms, any form of hormonal contraceptives, or
             abstinence) for the duration of the study and for 3 months following the last dose of
             study treatment.

         17. Male subjects must be sterile (biologically or surgically) or commit to the use of a
             reliable method of birth control (condoms with spermicide) for the duration of the
             study.

        Exclusion Criteria: Any subject who meets any of the following criteria should be excluded
        from the study:

          1. History of allergic reactions to any component of the ARX788.

          2. 2. History of seizure disorder.

          3. History of unstable central nervous system (CNS) metastases or seizure disorder
             related to the malignancy; however, those subjects who were treated for prior CNS
             metastases and who are asymptomatic may participate in the study as long as they are
             not receiving treatment with steroids.

          4. History of congestive heart failure, unstable angina pectoris, unstable atrial
             fibrillation, or cardiac arrhythmia.

          5. Grade 2 to 4 peripheral neuropathy (NCI CTCAE v 4.03).

          6. Non-manageable electrolyte imbalances including hypokalemia, hypocalcemia, or
             hypomagnesemia (Grade 2 or greater based on NCI CTCAE v 4.03).

          7. Any uncontrollable intercurrent illness, infection, or other conditions that could
             limit study compliance or interfere with assessments.

          8. Exposure to any other investigational or commercial anticancer agents or therapies
             administered with the intention to treat malignancy within 28 days before the first
             dose of the IMP.

          9. Significant surgical intervention within 21 days of the first dose of the IMP or with
             ongoing post-operative complications if more than 21 days.

         10. Radiotherapy administrated less than 21 days prior to the first dose of the IMP, or
             localized palliative radiotherapy administered less than 7 days prior to the first
             dose of the IMP, or radiotherapy induced toxicity of Grade 2 or greater based on NCI
             CTCAE v 4.03.

         11. Pregnancy or breast feeding.

         12. Refusal to use effective methods of contraception (see inclusion criteria for
             details).

         13. Legal incapacity/limited legal capacity for providing informed consent.