A Study of ASP2998 Given by Itself and Given With Standard Therapies in People With Solid Tumors

Inclusion Criteria: * For the ASP2998 monotherapy dose escalation (excluding urothelial and non-small cell lung cancer (NSCLC) tumor-specific backfill participants), the following criteria apply: * Participant has a confirmed diagnosis of locally advanced unresectable or metastatic solid tumors. * Participant has progressed on, is ineligible for, or has refused all available standard therapies (no limit to the number of prior treatment regimens). * Prior exposure to TROP2, stimulator of interferon genes (STING) agonist or topoisomerase I (TopI) directed therapy is allowed. * Participant must have one of the following malignancies: Urothelial carcinoma, NSCLC, Gastric/ gastroesophageal junction (GEJ) cancer, Breast cancer (human epidermal growth factor receptor 2 \[HER2\]-negative; local testing for HER2 status is acceptable). * For all tumor types, any component of neuroendocrine histology is ineligible. * For the ASP2998 NSCLC second line (2L)+ Monotherapy Dose Expansion Cohort(s) (including the tumor-specific backfill participants from the monotherapy dose escalation), the following criteria apply: * Participant has locally advanced unresectable or metastatic NSCLC with known programmed cell death-1 (PD-L1) status, without actionable oncogenic alteration (AGA), according to local testing. * Participant must have histologically or cytologically confirmed diagnosis of locally advanced unresectable or metastatic NSCLC that has progressed on or after receiving platinum-based chemotherapy and/or checkpoint inhibitors according to local/regional standard of care. * Participant is also eligible if there is disease progression within 12 months of receiving neoadjuvant or adjuvant therapy for resectable disease. * Participant must be eligible to receive treatment in 2L+ setting. * Participant must have had no more than 3 prior lines of therapy. * No prior exposure to TROP2, STING agonist or TopI directed therapy is allowed. * For the ASP2998 Urothelial Carcinoma Monotherapy Dose Expansion Cohort(s) (including the tumor-specific backfill participants from the monotherapy dose escalation), the following criteria apply: * Participant must have histologically or cytologically confirmed diagnosis of urothelial carcinoma (i.e., cancer of the bladder, renal pelvis, ureter or urethra) in locally advanced unresectable or metastatic setting that has progressed on a combination of enfortumab vedotin and pembrolizumab according to local/regional standard of care. Participant with urothelial carcinoma (transitional cell) with \< 50% squamous differentiation or mixed cell types is eligible. * Participant is also eligible if there is disease progression within 12 months of receiving adjuvant or neoadjuvant therapy for resectable disease. * Participant must be eligible to receive treatment in 2L+ setting. * Participant must have had no more than 3 prior lines of therapy. * No prior exposure to TROP2, STING agonist or TopI directed therapy is allowed. * For ASP2998 combination therapy (including the tumor-specific backfill participants from the combination therapy dose escalation), the following criteria apply for the NSCLC first line (1L) ASP2998 + Pembrolizumab + Carboplatin Dose Escalation and Expansion Cohort(s): * Participant has locally advanced unresectable or metastatic NSCLC (adenocarcinoma only, no mixed histology allowed), with known PD-L1 status, without AGA, according to local testing. * Participant is also eligible if there is disease progression \> 12 months after completing adjuvant or neoadjuvant therapy for resectable disease. * Participant has not received prior therapy for metastatic disease. * No prior exposure to TROP2, STING agonist or TopI directed therapy is allowed in dose escalation or dose expansion. * For ASP2998 combination therapy (including the tumor-specific backfill participants from the combination therapy dose escalation), the following criteria apply for the Urothelial Carcinoma 1L ASP2998 + Pembrolizumab + Enfortumab Vedotin Dose Escalation and Expansion Cohort(s): * Participant must have histologically or cytologically confirmed diagnosis of urothelial carcinoma (i.e., cancer of the bladder, renal pelvis, ureter or urethra) in locally advanced unresectable or metastatic setting. Participant with urothelial carcinoma (transitional cell) with \< 50% squamous differentiation or mixed cell types is eligible. * Participant is also eligible if there is disease progression \> 12 months after completing adjuvant or neoadjuvant therapy for resectable disease. * Participant has not received prior therapy for metastatic disease. * No prior exposure to TROP2, STING agonist or TopI directed therapy is allowed in dose escalation or dose expansion. * For ASP2998 combination therapy (including the tumor-specific backfill participants from the combination therapy dose escalation), the following criteria apply for the NSCLC 2L+ ASP2998 + Pembrolizumab Dose Escalation Cohort(s): * Participant has locally advanced unresectable or metastatic NSCLC with known PD-L1 status, without AGA, according to local testing. * Participant has progressed on or after receiving platinum-based chemotherapy and/or checkpoint inhibitors according to local/regional standard of care. * Participant is also eligible if there is disease progression within 12 months of receiving neoadjuvant or adjuvant therapy for resectable disease. * Participant may be eligible to receive treatment in 2L+ setting. * Participant must have had no more than 3 prior lines of therapy. * Prior exposure to TROP2, STING agonist or TopI directed therapy is allowed. * For ASP2998 combination therapy (including the tumor-specific backfill participants from the combination therapy dose escalation), the following criteria apply for the Urothelial Carcinoma 2L+ ASP2998 + Pembrolizumab Dose Escalation Cohort(s): * Participant must have histologically or cytologically confirmed diagnosis of urothelial carcinoma (i.e., cancer of the bladder, renal pelvis, ureter or urethra) in locally advanced unresectable or metastatic setting that has progressed on a combination of enfortumab vedotin and pembrolizumab according to local/regional standard of care. Participant with urothelial carcinoma (transitional cell) with \< 50% squamous differentiation or mixed cell types is eligible. * Participant is also eligible if there is disease progression within 12 months of receiving adjuvant or neoadjuvant therapy for resectable disease. * Participant must be eligible to receive treatment in 2L+ setting. * Participant must have had no more than 3 prior lines of therapy. * Prior exposure to TROP2, STING agonist or TopI directed therapy is allowed. * For ASP2998 combination therapy (including the tumor-specific backfill participants from the combination therapy dose escalation), the following criteria apply for the Urothelial Carcinoma 2L+ ASP2998 + Enfortumab Vedotin Dose Escalation Cohort(s): * Participant must have histologically or cytologically confirmed diagnosis of urothelial carcinoma (i.e., cancer of the bladder, renal pelvis, ureter or urethra) in locally advanced unresectable or metastatic setting that has progressed on a combination of enfortumab vedotin and pembrolizumab according to local/regional standard of care. Participant with urothelial carcinoma (transitional cell) with \< 50% squamous differentiation or mixed cell types is eligible. * Participant is also eligible if there is disease progression within 12 months of receiving adjuvant or neoadjuvant therapy for resectable disease. * Participant must be eligible to receive treatment in 2L+ setting. * Participant must have had no more than 3 prior lines of therapy. * Prior exposure to TROP2, STING agonist or TopI directed therapy is allowed. * Participant has a predicted life expectancy ≥ 12 weeks. * Participant has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * 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's adverse events (AEs) (excluding alopecia) from prior anticancer therapy have improved to Grade 1 or baseline within 14 days prior to the first dose of study intervention. * Participant has adequate organ function as indicated by laboratory values (If a participant has received a recent blood transfusion, the laboratory tests must be obtained ≥ 14 days after any blood transfusion.) * Female participant is not pregnant and at least 1 of the following conditions apply: * Not a woman of childbearing potential (WOCBP) * WOCBP who has a negative serum pregnancy test and confirmed not pregnant by medical interview at screening and agrees to follow the contraceptive guidance from the time of informed consent through 7 months after final study intervention administration. * Female participant must not be breastfeeding or lactating starting at screening and throughout the investigational period and for 7 months after final study intervention administration. * Female participant must not donate ova starting at first administration of study intervention and throughout the investigational period and for 7 months after final study intervention administration. * Male participant must agree to use contraception with female partner(s) of childbearing potential (including breastfeeding partner) throughout the treatment period and for 4 months after final study intervention administration. * Male participant must agree to remain abstinent or use a condom with pregnant partner(s) for the duration of the pregnancy throughout the investigational period and for 4 months after final study intervention administration. * Male participant must not donate sperm during the treatment period and for 4 months after final study intervention administration. * Participant agrees not to participate in another interventional study while receiving study intervention in the present study/participating in the present study (participant who is currently in the follow-up period of an interventional clinical study is allowed). Exclusion Criteria: * Participant weighs \< 40 kg during screening. * Participant has known active central nervous system (CNS) metastases. NOTE: A participant with CNS metastases that have been treated with surgery and/or radiation therapy, who is no longer taking pharmacologic doses of glucocorticoids and is neurologically stable, is eligible. Prophylactic use of anticonvulsants is permitted. * Participant has any of the following: * Any history of recurrent Grade 3 AEs/ immune-related AEs (irAEs) or history of Grade 4 irAEs related to prior anticancer therapy. * Recurrent Grade 3 or Grade 4 toxicities related to prior anticancer therapy not improved to Grade ≤ 1 or baseline per National Cancer Institute Common Terminology Criteria for Adverse Events (NCI-CTCAE) v5.0 or higher at least 28 days prior to initiating screening. NOTE: Participant with chronic, stable Grade ≤ 2 toxicities is eligible if the toxicity has not worsened beyond Grade 2 for at least 3 months prior to C1D1 and is managed with standard of care treatment, and is considered by the investigator to be related to prior anticancer therapy. However, a participant who meets other exclusion criteria will be excluded from the study regardless of the above provisions. * Participant has active or prior autoimmune or inflammatory disorders requiring systemic anti-inflammatory or immunosuppressive therapy within the past 3 years. Participants with type 1 diabetes mellitus or endocrinopathies stably maintained on appropriate replacement therapy will not be excluded. * Participant has uncontrolled diabetes mellitus. For cohorts receiving enfortumab vedotin, uncontrolled diabetes is defined as hemoglobin A1c (HbA1c) of ≥ 8% or HbA1c of 7% to \< 8% with associated diabetes symptoms (polyuria or polydipsia). * Participant has leptomeningeal disease as a manifestation of the current malignancy. * Participant has a known additional malignancy that requires active treatment, with the exception of any of the following: * Locally curable malignancies that have been apparently cured with no recurrence in the past 2 years. * Adequately treated stage I cancer from which the participant is currently in remission and has been in remission for ≥ 2 years. * Any other cancer from which the participant has been disease-free for ≥ 5 years. * Participant has a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of first administration of study intervention. Inhaled or topical steroids and adrenal replacement doses ≤ 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. * Participant has jaundice or known current active liver disease from any cause, including hepatitis A (hepatitis A virus (HAV) immunoglobulin M (IgM) positive, but testing for hepatitis A viral load in screening is not required), hepatitis B (hepatis B virus (HBV) (hepatitis B surface antigen positive, or HBV DNA positive if HBsAg is negative and anti-HBs and/or anti-HBc positive)), or hepatitis C (HCV antibody positive, confirmed by HCV RNA). NOTE: screening for these infections should be conducted per local requirements. * Participant has a known history of human immunodeficiency virus (HIV) infection with acquired immunodeficiency syndrome (AIDS)-related complications. HIV testing will be conducted per local requirements. * Participant has clinically significant cardiac disease, defined as any of the following: * Clinically significant cardiac arrhythmias including bradyarrhythmia which are poorly controlled. Rate-controlled atrial fibrillation is permitted. * Congenital long QT syndrome. * corrected QT interval by Fridericia (QTcF) ≥ 470 msec at screening. Electrocardiograms (ECGs) will be performed in triplicate during screening; the average of the triplicate readings will be used in the calculation of QTc. If the QTc is prolonged in a participant with a pacemaker or a right sided bundle branch block, the participant may be enrolled. Participant with a left sided bundle branch block will be excluded. * History of clinically significant cardiac disease or congestive heart failure greater than New York Heart Association (NYHA) Class II or left ventricular ejection fraction (LVEF) measurement of \< 50% at baseline. Participant must not have had unstable angina (symptoms at rest) or new-onset angina within the last 3 months or myocardial infarction within the past 6 months. * Uncontrolled hypertension, defined as systolic blood pressure \> 160 mmHg or diastolic blood pressure \> 100 mmHg that has been confirmed by 2 successive measurements, despite optimal medical management. * Arterial or venous thrombotic or embolic events such as cerebrovascular accident (including transient ischemic attacks), deep vein thrombosis or pulmonary embolism within 3 months before start of study intervention. * Participant has a history of non-infectious interstitial lung disease (ILD)/pneumonitis, has current Grade ≥ 1 ILD/pneumonitis, or where suspected ILD/pneumonitis cannot be ruled out by imaging at screening. Participant with previously diagnosed Grade 1 radiation pneumonitis is allowed to be screened for the study. Radiation pneumonitis must be confined to the previously irradiated area of the lung and completely resolved. However, any participant with a history of radiation pneumonitis that required steroid treatment will be excluded, regardless of resolution. * Participant has inadequate pulmonary reserve due to pulmonary, heart or other disease. * Participant has a confirmed oxygen saturation (SpO2) \< 92% at screening. * Participant requires chronic oxygen supplementation therapy. * Participant has evidence of structural compromise to the trachea for any reason, including underlying malignancy. * Participant has had major surgery within 4 weeks prior to first dose of study intervention. * Participant currently has or has a history of Grade 2 or higher eye disorder, as per NCI-CTCAE v5.0 or higher. * Participant is at a significant risk of bleeding due to medical condition(s) or use of anticoagulants, or has a history of life-threatening bleeding (e.g., intracranial bleeding). * Participant has current peripheral neuropathy Grade 2 or higher (specific for enfortumab vedotin or carboplatin-containing cohorts only). * Participant has a history of Grade 2 or higher hearing loss (specific for the carboplatin-containing cohort only). * Participant has received prior TROP2 targeting agents, STING agonists or TopI inhibitor (exception: dose escalation cohorts in monotherapy and 2L+ combination therapy). * Participant has received prior anticancer therapy within 28 days or 5 half-lives, whichever is shorter, prior to the first dose of study intervention. * Participant has received prior radiation therapy within 14 days of the first dose of study intervention. Participant must have recovered from all radiation-related toxicities and not require corticosteroids. A 1-week washout is permitted for palliative radiation (≤ 3 weeks of radiotherapy) to non-CNS disease. * Participant has an active infection requiring intravenous antibiotics within 14 days prior to study intervention. * Participant is expected to require another form of anticancer therapy while on study intervention. * Participant is receiving anticoagulants (vitamin K antagonists or direct oral anticoagulants) or antiplatelet agents. Low dose aspirin is allowed. * Participant has received any investigational therapy within 28 days or 5 half-lives, whichever is shorter, prior to the first dose of study intervention. * Participant has any condition that makes the participant unsuitable for study participation. * Participant has a known or suspected hypersensitivity to study intervention or any components of the formulation used. * Participant has history of life-threatening (anaphylaxis) hypersensitivity reactions to monoclonal antibodies, bispecifics, immunomodulatory drugs or antibody-drug conjugates (ADCs).