The main aims of this study are:

• To check the safety of ASP1002 in people with certain solid tumors.
• To check if the people can tolerate ASP1002.
• To find a suitable dose of ASP1002. This study will be in 2 parts. In Part 1, different small groups of people will receive lower to higher doses of ASP1002. Any medical problems will be recorded at each dose. This is done to find suitable doses of ASP1002 to use in Part 2 of the study.

In Part 2, other different small groups of people will receive doses of ASP1002 that worked the best in Part 1.

People in this study will be adults with metastatic or locally advanced solid tumors with high levels of a protein called claudin 4. The people's cancer will have either spread to other parts of the body (metastatic) or spread to tissue close by (locally advanced).

They will have been previously treated with available standard therapies or refused to receive those treatments.

In both parts of the study, ASP1002 (the study treatment) will be given to people slowly through a tube into a vein. This is called an infusion. This will happen every week, every other week, or every 3 weeks, in treatment cycles. Treatment cycles may be 21 days or 28 days long. People in this study will continue treatment for up to 2 years until: they have medical problems that prevent them from continuing treatment; their cancer gets worse; they start other cancer treatment; they ask to stop treatment; they do not come back for treatment.

During the study, people will visit the clinic several times for a health check. This includes standard safety checks and reporting any medical problems. Every few weeks, the study doctors will check if each person's cancer has stayed the same or got worse. This will be done by scans (CT or MRI scans). Tumor samples will be taken during the study and people will have the option of giving a tumor sample after treatment has finished.

People will visit the clinic within 7 days after stopping treatment for a health check. Then, they may visit the clinic at 1 month and 3 months after stopping treatment for further health checks. People will have follow-up health checks for up to 1 year after their last dose of ASP1002.

Inclusion Criteria:

• Participant has locally-advanced (unresectable or metastatic solid tumor which is confirmed by available pathology records or current biopsy.

  1. For dose escalation, the participant must P the following malignancies (for all tumor types, any component of neuroendocrine histology is exclusionary):

     I. NSCLC - adenocarcinoma, squamous cell carcinoma and adenosquamous are included; large cell carcinoma and sarcomatoid carcinoma are excluded.

     Note: NSCLC Not Otherwise Specified will require documented discussion with the medical monitor prior to study entry II. UC II. CRC IV. Prostate adenocarcinoma V. Epithelial ovarian cancer (including fallopian tube cancer) VI. TNBC

     • TNBC defined as unequivocal TNBC histology (ER 1 negative/progesterone receptor-negative/HER2-negative). This is defined by < 1% expression of ER and progesterone receptor by IHC and that are, for HER2, either 0 to 1+ by IHC, or IHC 2+ and FISH negative (not amplified) as per current ASCO/CAP guidelines [Hammond et al, 2010].

  2. For dose expansion, the participant must have one of the following malignancies (for all tumor types, any component of neuroendocrine histology is not eligible):

     I. NSCLC - adenocarcinoma, squamous cell carcinoma and adenosquamous are included; large cell carcinoma and sarcomatoid carcinoma are excluded. Note: NSCLC Not Otherwise Specified will require documented discussion with the medical monitor prior to study entry.

     II. UC III. CRC IV. Tumor type for which a confirmed response was observed during dose escalation.

• Female participant is not pregnant, confirmed by pregnancy test (and medical evaluation by interview [UNIQUE to Japan]), and at least 1 of the following conditions apply:

  1. Not a woman of childbearing potential (WOCBP)
  2. WOCBP who agrees to follow the contraceptive guidance from the time of informed consent through at least 90 days after final study intervention administration.

• Participant has progressed, is intolerant, has refused, or there are no standard approved therapies that impart significant clinical benefit (no limit to the number of prior treatment regimens).

• Participant has accessible archival tumor tissue (< 6 months old) from either the primary tumor or a metastatic site, for which source and availability have been confirmed prior to study intervention; participants without available tissue should undergo a mandatory biopsy. If the participant is unable to undergo a biopsy due to safety concerns, enrollment into the study is at the discretion of the medical monitor. Participant should undergo a tumor biopsy during the treatment period as indicated in the schedule of assessments. Note: Tumor tissue collection (at screening/baseline and on-treatment) is optional for participants enrolled initially in dose levels 1 to 3 in dose escalation; however, protocol de-escalation and expansion of dose levels similar to dose levels 1 to 3 may require collection and processing of screening/baseline and on-treatment tumor samples.

• Participant has at least 1 measurable lesion per RECIST v1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions.

• Participant has an Eastern Cooperative Oncology Group (ECOG) Status of 0 or 1.

• Participants who have received radiotherapy must have completed this therapy (including stereotactic radiosurgery) at least 2 weeks prior to study intervention administration.

• Participant has predicted life expectancy >/= 12 weeks.

• Participant has adequate organ function prior to start of study intervention. If a participant has received a recent blood transfusion, the laboratory tests must be obtained >/=2 weeks after any blood transfusion.

• Female participant is not pregnant and at least 1 of the following conditions apply:

  • a. Not a woman of childbearing potential (WOCBP)
  • b. WOCBP who agrees to follow the contraceptive guidance from the time of informed consent through at least 90 days after final study intervention administration.

• Female participant must agree not to breastfeed starting at screening and throughout the study period and for 90 days after final study intervention administration.

• Female participant must not donate ova starting at first administration of study intervention and throughout 90 days after final study intervention administration.

• Male participant with female partner(s) of childbearing potential (including breastfeeding partner) must agree to use contraception throughout the treatment period and for 90 days after final study intervention administration.

• Male participant must not donate sperm during the treatment period and for 90 days after final study intervention administration.

• Male participant with pregnant partner(s) must agree to remain abstinent or use a condom for the duration of the pregnancy throughout the study period and for 90 days after final study intervention administration.

• Participant agrees not to participate in another interventional study while receiving study intervention in the present study.

Exclusion Criteria:

• Participant weighs < 40 kg.

• Participant has ongoing toxicity >/= grade 2 per the Common Terminology Criteria for Adverse Events (CTCAE) version 5.0 considered clinically significant and attributable to prior antineoplastic therapies.

• Participant has symptomatic CNS metastases or evidence of uncontrolled CNS disease even if asymptomatic (e.g. progression on scans). Participants with previously treated CNS metastases are eligible, if they are clinically stable and have no evidence of CNS progression by imaging for at least 4 weeks prior to start of study intervention and are not requiring immunosuppressive doses of systemic steroids (equivalent to > 10 mg per day of prednisone) for longer than 2 weeks.

• Participant has an active autoimmune disease. Participant with type 1 diabetes mellitus, endocrinopathies stably maintained on appropriate replacement therapy, or skin disorders (e.g., vitiligo, psoriasis or alopecia) not requiring systemic treatment are allowed.

• Participant has had a myocardial infarction or unstable angina within 6 months prior to the start of study intervention or currently has an uncontrolled illness including, but not limited to, symptomatic congestive heart failure, clinically significant cardiac disease, unstable angina pectoris, cardiac arrhythmia, complete left bundle branch block, obligate use of a cardiac pacemaker, long QT syndrome or right bundle branch block with left anterior hemiblock (bifascicular block).

• Participant has a corrected corrected QT interval (QTcF) interval (single electrocardiogram (ECG)) > 470 ms within 7 days prior to the first study intervention administration on day 1.

• Participant has left ventricular ejection fraction (LVEF) < 45% noted in screening echocardiogram (ECHO). Any clinically significant findings from this ECHO should be discussed with the medical monitor.

• Participant is known to have human immunodeficiency virus (HIV) infection. However, participants with HIV infection with CD4+ T cell counts >/=350 cells/μL and no history of acquired immunodeficiency syndrome (AIDS)-defining opportunistic infections within the past 6 months are eligible. Note: No HIV testing is required at screening unless mandated per local requirements.

• Participant has any of the following per screening serology test:

  • a. Hepatitis A virus antibodies immunoglobulin (IgM)
  • b. Positive hepatitis B surface antigen (HBsAg) or detectable hepatitis B Deoxyribonucleic Acid (DNA). Participant with negative HBsAg, positive hepatitis B core antibody (anti-HBc) and negative hepatitis B surface antibody (anti-HBs) are eligible if hepatitis B DNA is undetectable
  • c. hepatitis C virus (HCV) antibodies unless HCV Ribonucleic acid (RNA) is undetectable
  • d HCV antibodies, and antigens (UNIQUE to Japan), unless HCV RNA is undetectable.

• Participant has a history of drug-induced pneumonitis, interstitial lung disease (ILD), currently has pneumonitis, or a prior history of ILD or non-infectious pneumonitis requiring high-dose glucocorticoids.

  • UNIQUE to Japan: Participant has a history of interstitial pneumonia.

• Participant has an uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, any form of substance abuse or psychiatric illness/social situations that would limit compliance with study visits or requirements or a condition that could invalidate communication with the investigator.

• Participant has received a prior allogeneic bone marrow or solid organ transplant.

• Participant has had a major surgical procedure and has not completely recovered within 28 days prior to the start of study intervention.

• Participant with recent positive antigen test for Coronavirus Disease 2019 (COVID-19) within 10 days prior to study intervention administration. Note: Participants who are asymptomatic after 10 days from the first positive antigen test may be enrolled.

• Participant has received any investigational therapy or antineoplastic therapy or other immunotherapy within 21 days or 5 half-lives, whichever is shorter, prior to the first dose of study intervention. Note: Participants with prostate adenocarcinoma who do not have a bilateral orchiectomy should continue androgen deprivation therapy (ADT) during the study. A participant with epidermal growth factor receptor (EGFR), receptor tyrosine kinase (encoded by the gene ROS1), or anaplastic lymphoma kinase (ALK) mutation-positive NSCLC is allowed to remain on EGFR tyrosine receptor inhibitor, neurotrophic tyrosine receptor kinase inhibitor or ALK inhibitor therapy until 4 days prior to the start of study intervention administration.

• Participant requires or has received systemic steroid therapy or any other immunosuppressive therapy within 14 days prior to ASP1002 administration. Participants using a physiologic replacement dose of corticosteroids equivalent to 10 mg per day of prednisone or less are allowed, as is receiving a single dose of systemic corticosteroids, or receiving systemic corticosteroids as premedication for radiologic imaging contrast is eligible.

• Participant was discontinued from prior immunomodulatory therapy due to a grade >/=3 toxicity that was mechanistically related (e.g., immune-related) to the agent and deemed life-threatening.

• Participant is expected to require another form of antineoplastic therapy while on study intervention.

• Participant has another malignancy requiring active therapy; (other than those indicated in Inclusion Criterion No. 1).

• Participants who have received prior anti-CD137 therapy.

• Participant has received a live vaccine against infectious diseases within 28 days prior to initiation of study intervention.

• Participant has any condition makes the participant unsuitable for study participation.

• Participant has a known or suspected hypersensitivity to ASP1002 or any components of the formulation used.

Access to anonymized individual participant level data collected during the study, in addition to study-related supporting documentation, is planned for studies conducted with approved product indications and formulations, as well as products terminated during development. Studies conducted with product indications or formulations that remain active in development are assessed after study completion to determine if Individual Participant Data can be shared. Further details on Astellas' data sharing policy can be found at https://www.clinicaltrials.astellas.com/transparency/.

Access to participant level data is offered to researchers after publication of the primary manuscript (if applicable) and is available as long as Astellas has legal authority to provide the data.

Researchers must submit a proposal to conduct a scientifically relevant analysis of the study data. The research proposal is reviewed by an Independent Research Panel. If the proposal is approved, access to the study data is provided in a secure data sharing environment after receipt of a signed Data Sharing Agreement.