Participants in this study will receive ASN004 once every 3 or 4 weeks by intravenous infusion. The ASN004 dosing schedule may be modified based on emerging data and Safety Review Committee decision. The study will test various doses of ASN004 to find out the highest safe dose to test in future trials.

Eligible subjects will be sequentially enrolled in cohorts at escalated doses.

Eligible patients will be sequentially enrolled at escalating doses.

Dose escalation decisions will be based on the review of clinical safety and pharmacokinetic (PD) and pharmacodynamics (PD) data and agreed upon by the Sponsor and investigators.

The maximum tolerated dose (MTD) will have an estimated DLT rate of < 33%. Cohorts may be expanded at any dose level or at the MTD for further evaluation of safety, or PK parameters as required.

Inclusion Criteria

1. Provide written, voluntary informed consent prior to any -study specific procedure.

2. Histologically confirmed diagnosis of advanced malignant solid tumor.

3. All patients must agree to provide fresh or archival tumor tissue from the tumor lesion that has not been previously irradiated. Patients without archival tissue may only be enrolled if the patient consents to a screening biopsy and this procedure may be safely performed in the judgment of the Investigator.

4. Evidence of progressive disease.

5. For Dose Expansion patients, eligible tumor histologies will be limited to those malignancies known to have highest expression of 5T4 including colorectal, breast, ovarian, lung, liver, and renal carcinomas. A maximum of 3 prior cytotoxic chemotherapy regimens is permitted for advanced disease.

6. Failure of standard therapy or no standard therapy available.

7. Presence of at least 1 measurable target lesion by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 excluding previously irradiated lesions, bone metastasis, or pleural effusion as sole manifestations of disease. Dose escalation patients with evaluable (non-measurable) disease may be permitted to enroll with Medical Monitor approval.

8. Age of at least 18 years old.

9. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.

10. A male patient must agree to use contraception as detailed in this protocol during the treatment period and for at least 3 months after the last dose of study treatment and refrain from donating sperm during this period.

11. A female patient is eligible to participate if she is not pregnant, not breastfeeding, and at least 1 of the following conditions applies.

    i. Not a woman of childbearing potential (WOCBP) OR ii. A WOCBP who agrees to follow the contraceptive guidance during the treatment period and for at least 3 months after the last dose of study treatment.

12. Adequate organ function.

13. Patients with Mandatory 5T4 Expression: Patients replacing a previously enrolled non-5T4 expressing patient must consent to and provide fresh or archival tumor tissue to the central pathology laboratory for 5T4 immunohistochemistry (IHC) testing. To be eligible, the patient's tumor must be confirmed by the central pathology laboratory to express 5T4 (H score of ≥ 10).

14. Patient is willing and able to comply with all protocol required visits and assessments.

Exclusion Criteria

1. Hematologic malignancies and lymphomas.
2. Patients with known brain metastases unless the patient has a single lesion or multiple lesions whose sum of the longest diameter is ≤ 1 cm AND who are asymptomatic.
3. Serious concurrent medical conditions.
4. Patients with known history of left ventricular ejection fraction of < 50%.