A Study of ASP388B Given by Itself and With Standard Therapies in Participants With Solid Tumors

Inclusion Criteria: For the ASP388B monotherapy dose escalation (excluding the 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 B7-H3, STING agonist or TopI directed therapy is allowed. * Participant must have one of the following malignancies (for all tumor types, any compounds of neuroendocrine histology is ineligible): HNSCC, ESCC, mCRPC, sqNSCLC, SCLC * For mCRPC * Participants with histologically or cytologically confirmed mCRPC who are refractory to a novel antiandrogen therapy (including but not limited to abiraterone, enzalutamide and/or apalutamide) and have failed at least 1 (but not more than 2) taxane regimens (or who are deemed medically unsuitable to be treated with a taxane regimen or have actively refused treatment with a taxane regimen). * Participants must have undergone bilateral orchiectomy or must be on continuous ADT with a GnRH agonist or antagonist. * Total serum testosterone ≤ 50 ng/dL or 1.7 nmol/L * Evidence of progressive disease, defined as ≥ 1 PCWG3 criteria: PSA level ≥ 1 ng/mL that has increased on at least 2 successive occasions at least 1 week apart; Nodal or visceral progression as defined by RECIST v1.1 with PCWG3 modifications; Appearance of ≥ 2 new lesions in bone scan * Participants with mCRPC can be enrolled without measurable disease. * For sqNSCLC * Participants with known EGFR, ALK, ROS, BRAF or other actionable mutations are eligible if treated with mutation targeted therapy and have progressed, relapsed or discontinued treatment due to toxicity. * For SCLC * Metastatic or extensive stage (EC-SCLC) For the ASP388B 2L+HNSCC monotherapy dose expansion (including the tumor-specific backfill participants from the monotherapy dose escalation), the following criteria apply: * Participant has histologically or cytologically confirmed HNSCC. * Tumors arising from the nasopharynx are excluded. * Known PD-1/PD-L1 status and any HPV status is eligible. * Participant has evidence of radiographic progression on or after the last regimen received. * Participant has locally advanced or metastatic disease that is not amenable to curative intent treatment. * Participant has progressed, relapsed or discontinued treatment due to toxicity after local guidelines/SOC regimen for locally advanced or metastatic disease, and has received ≤ 3 prior lines of anticancer therapy in the locally advanced or metastatic setting. * Neoadjuvant or adjuvant cytotoxic regimens will count as a prior regimen if relapsed or progressed ≤ 6 months after completion. * No prior exposure to B7-H3, STING agonist or TopI directed therapy is allowed. For the ASP388B 2L+ESCC monotherapy dose expansion (including the tumor-specific backfill participants from the monotherapy dose escalation), the following criteria apply: * Participant has histologically or cytologically confirmed ESCC. * Known PD-1/PD-L1 status and any HER2 status is eligible. * Participant has evidence of radiographic progression on or after the last regimen received. * Participant has locally advanced or metastatic disease that is not amenable to curative intent treatment. * Participant has progressed, relapsed or discontinued treatment due to toxicity after local guidelines/SOC regimen for locally advanced or metastatic disease, and has received ≤ 3 prior lines of anticancer therapy in the locally advanced or metastatic setting. * Neoadjuvant or adjuvant cytotoxic regimens will count as a prior regimen if relapsed or progressed ≤ 6 months after completion. * No prior exposure to B7-H3, STING agonist or TopI directed therapy is allowed. For the ASP388B 1L HNSCC (Excluding NPC and Salivary Gland Tumors) combination therapy dose escalation and expansion (including the tumor-specific backfill participants from combination therapy dose escalation), the following criteria apply: (ASP388B + Pembrolizumab + Carboplatin + 5-FU): * Participant has histologically or cytologically confirmed HNSCC excluding nasopharyngeal cancer (NPC) and salivary gland tumors. * Known PD-1/PD-L1 status and any HPV status is eligible * Participant has recurrent or metastatic disease that is incurable by local therapies. * Participant has had no prior systemic therapy administered with the exception of systemic therapy completed \> 6 months prior if given as part of multimodal treatment with curative intent for nonmetastatic disease stages. * No prior exposure to B7-H3, STING agonist or TopI directed therapy is allowed. For the ASP388B 1L ESCC combination therapy dose escalation and expansion (including the tumor-specific backfill participants from combination therapy dose escalation), the following criteria apply: (ASP388B + Pembrolizumab + Oxaliplatin + 5-FU): * Participant has histologically or cytologically confirmed ESCC. * Known PD-1/PD-L1 status and any HER2 status is eligible * Participant has had no prior systemic therapy administered with the exception of systemic therapy completed \> 6 months prior if given as part of multimodal treatment with curative intent for nonmetastatic disease stages. * No prior exposure to B7-H3, STING agonist or TopI directed therapy is allowed. For the ASP388B 1L ESCC combination therapy dose escalation and expansion * Participant has a predicted life expectancy ≥ 12 weeks. * 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 ECOG performance status of 0 or 1. * 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 urine or serum pregnancy test at screening with a medical interview and agrees to follow the contraceptive guidance from the time of informed consent through at least 7 months after final study intervention administration or after at least 9 months for participants with 1L ESCC receiving combination therapy, or per local labeling requirements, whichever is longer. * Female participant must not be breastfeeding or lactating starting at screening and throughout the investigational period and for 5 half-lives (approximately 7 months after final study intervention administration or after at least 9 months for participants with 1L ESCC receiving combination therapy, or per local labeling requirements, whichever is longer). * 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 or after at least 9 months for participants with 1L ESCC receiving combination therapy, or per local labeling requirements, whichever is longer. * 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 or after at least 9 months for participants with 1L ESCC receiving combination therapy, or per local labeling requirements, whichever is longer. Exclusion Criteria: * Participant weighs \< 40 kg during screening. * Participant has known active central nervous system (CNS) metastases. NOTE: A participant with CNS metastases who has 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 immune-related AEs (irAEs) or history of Grade 4 irAEs related to prior anticancer therapy. * Participant has active or prior autoimmune or inflammatory disorders requiring systemic therapy within the past 2 years including inflammatory skin conditions, inflammatory bowel disease (e.g., ulcerative colitis or Crohn's disease), diverticulitis (with the exception of diverticulosis), celiac disease, systemic lupus erythematosus, Sarcoidosis syndrome, Wegener syndrome (granulomatosis with polyangiitis), Graves' disease, rheumatoid arthritis, hypophysitis or uveitis. The following are exceptions to this criterion: * Participant with type 1 diabetes mellitus * Participant with vitiligo or alopecia * Participant with endocrinopathies stably maintained on appropriate replacement therapy * Participant with any chronic skin condition that does not require systemic therapy * 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: * Adequately treated basal or squamous cell skin cancer, superficial bladder cancer or carcinoma in situ of the cervix or breast * 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 known history of HIV infection with 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 and ventricular arrhythmia, which are poorly controlled; cardiomyopathy or moderate or severe valvular disease. NOTE: Rate-controlled atrial fibrillation is permitted. * Congenital long QT syndrome. * QTcF ≥ 470 msec at screening. ECGs will be performed in triplicate during screening; the average of the triplicate readings will be used in the calculation of QTcF. If the QTcF is prolonged in a participant with a pacemaker or a right-sided bundle branch block, the participant may be enrolled in the study if confirmed by the sponsor's medical monitor. Participant with a left-sided bundle branch block will be excluded. * History of clinically significant cardiac disease or congestive heart failure greater than NYHA Class II or LVEF measurement of \< 50% at baseline. Participant must not have had acute coronary syndrome, new-onset angina or coronary revascularization (PCI/CABG) within the past 12 months. * Uncontrolled hypertension, defined as systolic BP \> 160 mmHg or diastolic BP \> 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 the 3 months before start of study intervention. * Presence of cardiac injury syndromes: recent cardiac surgery, pacemaker/implantable cardioverter defibrillator insertion, ablation within 3 months prior to screening, recent PCI, blunt or penetrating chest trauma * Presence or history of pericarditis (acute, recurrent or restrictive), myocarditis or any pericardial effusion requiring drainage or other invasive procedures * History of pericardial tamponade, pericardial involvement associated with connective tissue diseases, sarcoidosis, vasculitis; congenital absence of defect of pericardium; aortic dissection with blood tracking into the pericardial space (hemopericardium/tamponade); iatrogenic hemopericardium (e.g., catheter perforation) * Significantly elevated cardiac biomarkers (troponins and NT-proBNP) that require cardiology referral at screening * Participant has a history of pleurodesis with impaired lung mechanics, recent (\< 6 weeks) pleurodesis or pleural surgery (decortication, pleurectomy), drug-induced fibrosing ILD, trapped lung, complicated pleural effusion, uncontrolled malignant pleural effusion, idiopathic pulmonary fibrosis, pneumonectomy, organizing pneumonia, drug-induced pneumonitis, idiopathic pneumonitis, noninfectious ILD/pneumonitis, fibrotic lung disease or connective tissue disorder with pulmonary involvement. Any participant with a history of radiation pneumonitis that required treatment (e.g., steroid) will be excluded, regardless of resolution. NOTE: Participant with previously diagnosed Grade 1 radiation pneumonitis is allowed to be screened for the study. However, radiation pneumonitis must be confined to the previously irradiated area of the lung and be completely resolved. * Participant has current Grade ≥ 1 ILD/pneumonitis, evidence of active pneumonitis on screening chest CT scan, or suspected ILD/pneumonitis that cannot be ruled out by imaging at screening. NOTE: If participant requires intermittent use of bronchodilators, inhaled steroids or local steroid injections, they will not be excluded. * Participant has pericardial disease related to prior radiation therapy. * Participant has a confirmed SpO2 \< 92% at screening. * Participant requires chronic oxygen supplementation therapy inclusive of noninvasive ventilation or bilevel positive airway pressure. * Participant has any lung or heart disease (e.g., asthma, COPD, congestive heart failure) with uncontrolled symptoms or recent exacerbation or which may confound pulmonary safety assessments. * Participant is at a significant risk of bleeding due to medical condition(s) or recent major bleeding (e.g., bleeding in critical site or requiring transfusions). * Participant has current peripheral neuropathy Grade ≥ 2 (specific for platinum-containing cohorts only). * Participant has a history of Grade ≥ 2 hearing loss (specific for platinum-containing cohorts only). * Participant has received any strong inhibitors of CYP3A and CYP1A2 within 1 week or 5 half-lives (whichever is longer) or strong inducers of CYP3A within 2 weeks or 5 half-lives (whichever is longer) before the first dose of ASP388B. * Participant has received prior B7-H3 targeting agents, STING agonists or TopI inhibitor (exception: monotherapy dose escalation cohorts). * Participant has received prior radiation therapy within 2 weeks 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 is receiving anticoagulants (vitamin K antagonists or direct oral anticoagulants) or antiplatelet agents. Low dose aspirin is allowed. * Participant has received prior immuno-oncology anticancer therapy within 6 weeks prior to the first dose of study intervention. Participant has received any other prior anticancer therapy within 28 days or 5 half-lives, whichever is longer, of the first dose of study intervention.