Inclusion Criteria:  Participant has locally-advanced (unresectable) or metastatic solid tumor malignancy that is confirmed by available pathology records or current biopsy. Participant must also have received all standard therapies (unless the therapy is contraindicated or intolerable) appropriate to provide clinical benefit for his/her specific tumor type. However, participants with metastatic melanoma who have not received checkpoint inhibitors [CPIs] (i.e., CPIs naive) may enroll in the Phase 2 Combination Therapy Arm Dose Expansion Cohort to receive CPI: Pembrolizumab. Participant must be diagnosed with solid tumor known to express WT1 antigen such as, but not limited to melanoma, ovarian cancer or Colorectal Cancer (CRC). Participant consents to provide an archival tumor specimen in a tissue block or unstained serial slides, if available, prior to study treatment. Participant has an Eastern Cooperative Oncology Group (ECOG) Performance Status of ≤ 2. Participant's last dose of prior antineoplastic therapy, including any immunotherapy, was 21 days or 5 half-lives, whichever is shorter, prior to initiation of IP administration. A participant with BRAF gene, epidermal growth factor receptor (EGFR) or anaplastic lymphoma kinase (ALK) mutation positive non-small cell lung carcinoma is allowed to remain on epidermal growth factor receptor (EGFR) tyrosine kinase inhibitor (TKI) or anaplastic lymphoma kinase (ALK) or BRAF inhibitor therapy until 4 days prior to the start of Investigational Product (IP) administration. Participant has completed any radiotherapy (including stereotactic radiosurgery) at least 2 weeks prior to IP administration. Participant's Adverse Events (AEs) (excluding alopecia) from prior therapy have improved to grade 1 or baseline within 14 days prior to start of IP. Participant has adequate organ function prior to start of IP. If a participant has received a recent blood transfusion, the laboratory tests must be obtained ≥ 4 weeks after any blood transfusion.  A female participant is eligible to participate if she is not pregnant and at least 1 of the following conditions applies:  Not a woman of childbearing potential (WOCBP) OR WOCBP who agrees to follow the contraceptive guidance from the time of informed consent through at least 6 months after the final IP administration. Female participant must agree not to breastfeed starting at screening and throughout the IP and for 180 days after the final IP administration. Female participant must not donate ova starting at screening and throughout the IP and for 180 days after the final IP administration. A male participant with female partner(s) of childbearing potential (including breastfeeding partner) must agree to use contraception throughout the treatment period and for at least 180 days after the final IP administration. Male participant must not donate sperm during the treatment period and for 180 days after the final IP 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 180 days after the final IP administration. Participant agrees not to participate in another interventional study while receiving IP.  Additional Inclusion Criteria for Participants in the Expansion Cohorts:  Participant meets one of the following:  Participant has the tumor type for which a confirmed response was observed in a monotherapy or combination therapy dose escalation (for melanoma, ovarian cancer and Colorectal Cancer [CRC] only) cohort; OR For tumor specific expansion cohorts of ASP7517 or ASP7517 with pembrolizumab, participant has the applicable tumor type melanoma, ovarian cancer, CRC. Participant has at least 1 measurable lesion per response evaluation criteria in solid tumors (RECIST) v1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. Participant consents to provide a tumor specimen in a tissue block or unstained serial slides obtained within 56 days prior to first dose of IP. If a recent tissue sample cannot be provided due to medical or safety concerns, enrollment into the study must be discussed with the medical monitor. Participant consents to undergoing a tumor biopsy (core tissue biopsy or excision) during the treatment period as indicated in the schedule of assessments if predose biopsy is available and if medically feasible.  Exclusion Criteria:  Participant weighs < 45 kg at screening. Participant has received investigational therapy (other than an investigational EGFR TKI in a participant with EGFR activating mutations or ALK or BRAF inhibitor in a participant with an ALK mutation) within 21 days or 5 half-lives, whichever is shorter, prior to start of IP. Participant requires or has received systemic steroid therapy or any other immunosuppressive therapy within 14 days prior to Cycle 1 Day 1. Participants using a physiologic replacement dose of hydrocortisone or its equivalent (defined as up to 30 mg per day of hydrocortisone up to 10 mg per day of prednisone) are allowed. Participant has symptomatic central nervous system (CNS) metastases or participant has evidence of unstable CNS metastases 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 IP and are not requiring immunosuppressive doses of systemic steroids (> 30 mg per day of hydrocortisone or > 10 mg per day of prednisone or equivalent) for longer than 2 weeks. Participant has an active autoimmune disease. Participants 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 was discontinued from prior immunomodulatory therapy due to a grade ≥ 3 toxicity that was mechanistically related (e.g., immune related) to the agent. Participant has known history of serious hypersensitivity reaction to a known ingredient of ASP7517 or pembrolizumab or severe hypersensitivity reaction to treatment with another monoclonal antibody. Participant has a known history of human immunodeficiency virus. Participant with known history of positive hepatitis B surface antigen or isolated hepatitis B core antibody (including acute HBV or chronic HBV) or hepatitis C ([HCV] ribonucleic acid [RNA] detected by qualitative assay). Hepatitis C RNA testing is not required in participants with negative hepatitis C antibody testing. Participant has received a live vaccine against infectious diseases within 28 days prior to initiation of IP. Participant has a history of drug-induced pneumonitis (interstitial lung disease), a history of (non-infectious) pneumonitis that required steroids, radiation pneumonitis or currently has pneumonitis. Participant has an infection requiring systemic therapy within 14 days prior to IP. Participant has received a prior allogeneic bone marrow or solid organ transplant. Participant is expected to require another form of antineoplastic therapy while on IP. Participant has had a myocardial infarction or unstable angina within 6 months prior to the start of IP or currently has an uncontrolled illness including, but not limited to symptomatic congestive heart failure, clinically significant cardiac disease, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. Participant has a clinically significant abnormal electrocardiogram at screening. Participant has symptomatic cardiovascular disease within the preceding 12 months unless cardiology consultation and clearance has been obtained for study participation, including but not limited to the following: significant coronary artery disease (e.g., requiring angioplasty or stenting), acute myocardial infarction or unstable angina pectoris < 3 months prior screening, uncontrolled hypertension, clinically significant arrhythmia or congestive heart failure (New York Heart Association grade ≥ 3). Any condition that makes the participant unsuitable for study participation. Participant has had a major surgical procedure and has not completely recovered within 28 days prior to the start of IP. Participant has a prior malignancy active (i.e., requiring treatment of intervention) within the previous 2 years prior to the screening visit, except for locally curable malignancies that have been apparently cured, such as basal or squamous cell skin cancer, superficial bladder cancer or carcinoma in situ of the cervix or breast. Participants with organ confined prostate cancer with no evidence of recurrent or progressive disease are eligible if hormonal therapy has been initiated or the malignancy has been surgically removed or treated with definitive radiotherapy. Participant has International Normalized Ration (INR) > 1.5 x Upper Limits of Normal (ULN) and/or activated partial thromboplastin time (aPTT) > 1.5 x institutional normal limits.  Additional Exclusion Criteria for Participants in Combination Expansion Cohorts:  Participants with metastatic CRC with documented microsatellite instability-high (MSI-H) or mismatch repair (MMR) deficient who have received prior treatment with PD-1 or programmed death-ligand (PD-L1) inhibitors such as nivolumab or pembrolizumab. CPI naïve metastatic melanoma participants who have received PD-1 or PD-L1 inhibitors, such as nivolumab or pembrolizumab. Participants with metastatic ovarian cancer with documented MSI-H or MMR deficient who have received PD-1or PD-L1 inhibitors, such as nivolumab or pembrolizumab.