A Study of ASP1948, Targeting an Immune Modulatory Receptor as a Single Agent and in Combination With a PD-l Inhibitor (Nivolumab or Pembrolizumab) in Subjects With Advanced Solid Tumors

Inclusion Criteria: * Subject has locally-advanced (unresectable) or metastatic solid tumor malignancy (no limit to the number of prior treatment regimens) that is confirmed by available pathology records or current biopsy, and has received all standard therapies (unless the therapy is contraindicated or intolerable) felt to provide clinical benefit. * Subject has an Eastern Cooperative Oncology Group (ECOG) performance status of 0, or 1. * Subject's last dose of prior antineoplastic therapy, including any immunotherapy, was at least 21 days prior to initiation of study drug administration. A subject with epidermal growth factor receptor (EGFR) or anaplastic lymphoma kinase (ALK) mutation-positive NSCLC is allowed to remain on EGFR tyrosine kinase inhibitor (TKI) or ALK inhibitor therapy until 4 days prior to the start of study drug administration. * Subject has completed any radiotherapy (including stereotactic radiosurgery) at least 14 days prior to study drug administration. * Subject with metastatic castration-resistant prostate cancer (mCRPC) (positive scan and/or soft tissue disease documented by computed tomography/magnetic resonance imaging) meets both of the following: * Subject has serum testosterone ≤ 50 ng/dL at screening. * Subject has had an orchiectomy or plans to continue androgen deprivation therapy (ADT) for the duration of study treatment. * Subject has adequate organ function as indicated by laboratory values. (If a subject has received a recent blood transfusion, the laboratory tests must be obtained ≥ 28 days after any blood transfusion.) Subjects can be on a stable dose of erythropoietin (≥ approximately 3 months). Note: Growth factors, colony stimulating factors are not permitted in the screening period. * Female subject must either: * Be of non-childbearing potential: post-menopausal (defined as at least 1 year without any menses for which there is no other obvious pathological or physiological cause) prior to screening, or; documented surgically sterile (e.g., hysterectomy, bilateral salpingectomy, bilateral oophorectomy). * Or, if of childbearing potential: Agree not to try to become pregnant during the study treatment and for 6 months after the final study drug administration; and have a negative urine or serum pregnancy test prior to study drug administration; and if heterosexually active, agree to consistently use 1 form of highly effective birth control starting at screening and throughout the study treatment and 6 months after the final study drug administration. * Female subject must agree not to breastfeed starting at screening and throughout the study treatment, and for 6 months after the final study drug administration. * Female subject must not donate ova starting at screening and throughout the study treatment, and for 6 months after the final study drug administration. * A sexually active male subject with female partner(s) who are of childbearing potential is eligible if : * The male subject agrees to use a male condom starting at screening and continues throughout the study treatment, and for 6 months after the final study drug administration. * The male subject has not had a vasectomy or is not sterile, as defined below and the subject's female partner(s) is utilizing 1 form of highly effective birth control starting at screening and continuing throughout the study treatment and for 6 months after the final study drug administration. * Male subject must not donate sperm starting at screening and throughout the study treatment, and for 6 months after the final study drug administration. * Male subject with a pregnant or breastfeeding partner(s) must agree to remain abstinent or use a condom for the duration of the pregnancy or time partner is breastfeeding throughout the study treatment and for 6 months after the final study drug administration. * Subject agrees not to participate in another interventional study while receiving study drug (subjects who are currently in the follow-up period of an interventional clinical trial are allowed). Additional Inclusion Criteria for Subjects in the Expansion Cohorts: * Subject has at least 1 measurable lesion per RECIST 1.1. The measureable lesion must be outside the field of radiation if subject had prior radiotherapy. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. Subjects with mCRPC who do not have measurable lesions must have at least 1 of the following: * Progression with 2 or more new bone lesions, or * Prostate specific antigen (PSA) progression (defined as a minimum of 3 rising PSA levels with an interval of ≥ 1 week between each determination) within 6 weeks prior to study drug administration and a PSA value at the screening visit ≥ 2 ng/mL. * Subject consents to provide available tumor specimen in a tissue block or unstained serial slides obtained within 8 to 56 days prior to first dose of study treatment. Note: This does not apply to subjects with mCRPC who do not have measurable disease. * Subject is an appropriate candidate for tumor biopsy and consents to undergoing a tumor biopsy (core needle biopsy or excision) during the treatment period. Note: This does not apply to subjects with mCRPC who do not have measurable disease. * Subject meets one of the following: * Subject has the tumor type for which a confirmed response was observed in a monotherapy or in combination with nivolumab dose escalation or RP2D cohort; or * ASP1948 monotherapy or in combination with pembrolizumab expansion cohort is opened due to achieving predicted efficacious exposure, subject has squamous cell carcinoma of the head and neck (SCCHN); or * RP2D monotherapy cohort is opened and subject has NSCLC, mCRPC, ovarian cancer, pancreatic cancer or breast cancer; or * RP2D combination with pembrolizumab expansion cohort, is opened and subject has NSCLC (all PD-L1 status), NSCLC PD-L1 high\*, ovarian cancer, colorectal cancer, or breast cancer. * NSCLC with PD-L1 high expressing tumor as determined by immunohistochemistry at a central laboratory during the screening period. Additional Inclusion Criteria for Re-treatment: Subjects may be eligible for study drug re-treatment if the study remains open and the subject continues to meet all of the eligibility criteria above (except prior use of this drug) and the following conditions: * Subject stopped initial treatment with ASP1948 or ASP1948 in combination with nivolumab or pembrolizumab after attaining a confirmed CR or PR or SD. * Subject experienced a confirmed disease progression by iRECIST (iCPD) after stopping their initial treatment with ASP1948 or ASP1948 in combination with nivolumab or pembrolizumab. * Subject did not receive any prohibited anti-cancer treatment since the last dose of ASP1948 or ASP1948 in combination with nivolumab or pembrolizumab. * Subject did not experience a toxicity that met the discontinuation criteria during the initial treatment with ASP1948 or ASP1948 in combination with nivolumab or pembrolizumab. Exclusion Criteria: * Subject weighs \< 45 kg. * Subject has received investigational therapy (other than an investigational epidermal growth factor receptor (EGFR) tyrosine kinase inhibitor (TKI) in a subject with EGFR mutations or ALK inhibitor in a subject with an ALK mutation) within 21 days prior to start of study drug. * Subject requires or has received systemic steroid therapy or any other immunosuppressive therapy within 14 days prior to study drug administration. Subjects using a physiologic replacement dose of hydrocortisone or its equivalent(defined as up to 30 mg per day of hydrocortisone, 2 mg per day of dexamethasone or up to 10 mg per day of prednisone) are allowed. Note: Corticosteroids for prophylaxis (e.g., contrast dye allergy) or for brief treatment of conditions not related to study treatment (e.g., delayed-type hypersensitivity reaction caused by a contact allergen) is also allowed. * Subject has symptomatic central nervous system (CNS) metastases or subject has evidence of unstable CNS metastases even if asymptomatic (e.g., progression on scans). Subjects with previously treated CNS metastases are eligible, if the subject is clinically stable and has no evidence of CNS progression by imaging for at least 28 days prior to start of study treatment and are not requiring immunosuppressive doses of systemic steroids (\> 30 mg per day of hydrocortisone, \> 2 mg per day of dexamethasone or \> 10 mg per day of prednisone or equivalent) for longer than 14 days. * Subject has leptomeningeal disease as a manifestation of the current malignancy. * Subject has an active autoimmune disease that has required systemic treatment in the past 2 years. Subjects with type 1 diabetes mellitus, stable endocrinopathies maintained on appropriate replacement therapy and skin disorders (e.g., vitiligo, psoriasis or alopecia) not requiring systemic treatment are allowed. * Subject was discontinued from prior immunomodulatory therapy due to a Grade ≥ 3 toxicity that was mechanistically related (e.g., immune related) to the agent. * Subject has known history of serious hypersensitivity reaction to a known ingredient of ASP1948, nivolumab or pembrolizumab or severe hypersensitivity reaction to treatment with another monoclonal antibody. * Subject with positive Hepatitis B virus antibodies and surface antigen (indicating acute Hepatitis B virus (HBV) or chronic HBV) or Hepatitis C (HCV ribonucleic acid (RNA) \[(qualitative or quantitative)\]. Hepatitis C RNA testing is not required in subjects with negative Hepatitis C antibody testing. Hepatitis B virus antibodies are not required in subjects with negative Hepatitis B surface antigen. * Subject has received a live vaccine against infectious diseases within 28 days prior to initiation of study treatment. * Subject 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. * Subject has an active infection requiring systemic therapy within 14 days prior to study drug treatment. * Subject is expected to require another form of antineoplastic therapy while on study treatment. * Subject has an uncontrolled intercurrent illness including, but not limited to cardiac arrhythmia or psychiatric illness/social situations that would limit compliance with study requirements. * Subject's AEs (excluding alopecia) from prior therapy have not improved to Grade 1 or baseline within 14 days prior to start of study treatment. * Subject has significant cardiovascular disease including: * Subject has inadequately controlled hypertension (defined as systolic blood pressure \> 150 and/or diastolic blood pressure \> 100 mmHg on antihypertensive medications). * Subject has a history of myocardial infarction or unstable angina within 6 months prior to day 1. * Subject has New York Heart Association Class II or greater chronic heart failure (CHF). * History of cerebrovascular accident (CVA) or transient ischemic attack (TIA) within 6 months prior to study treatment. * Subject has significant vascular disease (e.g., aortic aneurysm requiring surgical repair or recent peripheral arterial thrombosis) within 6 months prior to study treatment. * Subject has a history of hemoptysis (bright red blood of ½ teaspoon or more per episode) within 12 weeks prior to study treatment. * Subject has evidence of a bleeding diathesis or significant coagulopathy. * Subject has inadequate recovery from prior surgical procedure or has had a major surgical procedure, open biopsy or significant traumatic injury within 28 days prior to day 1, or anticipates the need for a major surgical procedure during the course of the study or minor surgery within 7 days of starting study treatment. * Subject has initiated new treatment with medications that affect the coagulation cascade with an international normalized ratio (INR) ≥ 2 such as vitamin K antagonists, heparins and direct thrombin inhibitors or the use of factor Xa inhibitors within 28 days prior to the start of study treatment. Note: If the subject started receiving such medications more than 28 days prior to the start of study treatment and needs to continue, this is allowed. However, new anticoagulation may not be initiated within 28 days prior to the start of study treatment. * Subject has any condition that makes the subject unsuitable for study participation. * Subject has a known history of human immunodeficiency virus (HIV) infection. No HIV testing is required unless mandated by local health authority. * Subject has had an allogeneic tissue solid organ transplant. * Subject has known history of COVID-19 positive polymerase chain reaction (PCR) test within 4 weeks prior to start of study treatment. Additional Exclusion Criteria for Subjects in Expansion Cohorts: * Subject has a prior malignancy active (i.e., requiring treatment or intervention) within the previous 2 years, except for locally curable malignancies that have been apparently cured, which are allowed, such as basal or squamous cell skin cancer, superficial bladder cancer or carcinoma in situ of the cervix or breast. * Subject has received prior treatment with a neuropilin-1 (NRP1) inhibitor. Additional Exclusion Criteria for Re-treatment: * Subjects who have completed 40 weeks (ASP1948 monotherapy or combination therapy with nivolumab cohorts) or 57 weeks (ASP1948 combination therapy with pembrolizumab) of follow-up with disease control are not eligible for retreatment. * Subject currently has an ongoing Adverse Event (AE) related to the initial ASP1948 or ASP1948 in combination with nivolumab or pembrolizumab treatment that meets the criteria for treatment interruption or discontinuation.