A Study of Vobramitamab Duocarmazine in Participants With Metastatic Castration Resistant Prostate Cancer and Other Solid Tumors

Inclusion Criteria: * Part 1 only: Histologically confirmed adenocarcinoma of the prostate without evidence of neuroendocrine differentiation, signet cell, or small cell features. * Part 2 only: Histologically confirmed SCC or the anus, melanoma, HNSCC, squamous NSCLC, or SCLC. * Part 1 only: Received 1 prior ARAT for metastatic or non-metastatic, castration-sensitive or castration-resistant prostate cancer. A second ARAT regimen of \<60 days used as bridging to lutetium-177 is permitted. Up to 3 total prior lines of therapy for mCRPC are permitted.. * Part 2 only: At least 1 prior line of systemic therapy for unresectable or metastatic disease and no more than 2 prior lines of cytotoxic chemotherapy. Participants with HNSCC or melanoma must have received prior PD-1 or PD-L1 inhibitor for advanced or metastatic disease. * All participants must have ≥ 1 metastatic lesion, according to RECIST 1.1 or PCWG3 criteria, that is present on magnetic resonance imaging (MRI), computed tomography (CT), or bone scan obtained ≤ 28 days prior to initiation of study treatment. * All participants must have tumor progression, according to disease-specific criteria, following their most recent anti-cancer therapy. * All participants must have and available archival or formalin-fixed paraffin-embedded (FFPE) tumor tissue sample for participants with metastasis to internal organs * All participants have acceptable physical condition and laboratory values. * All participants of childbearing potential must agree to use highly effective methods of birth control. * All participants must not be pregnant, planning to be pregnant, or breastfeeding. Exclusion Criteria: * Any underlying medical or psychiatric condition impairing participant's ability to receive, tolerate, or comply with the planned treatment or study procedures. * Part 1 only: Received \>1 prior taxane-containing regimen for prostate cancer. A second taxane regimen of \<60 days used as bridging for lutetium-177 is permitted. * Part 1 only: Received \>3 total prior therapies for mCRPC * Part 1 only: Participants with known BRCA or ATM mutation (germline or somatic) are not eligible unless they received prior treatment with a PARP inhibitor where available, indicated and tolerated. * Another hematologic or solid tumor ≥ stage 1 malignancy that completed surgery, last dose of radiotherapy, or last dose of systemic anti-cancer therapy ≤ 2 years from first dose of study treatment. Participants who had curative therapy for non-melanomatous skin cancer or for localized malignancy are eligible. * Untreated, symptomatic central nervous system (CNS) metastasis. * Prior treatment with any B7-H3 targeted agent for cancer, * Contradictions to the use of corticosteroid treatment * Prior stem cell, tissue, or solid organ transplant. * Part 1 only: Use of products that have published anti-prostate cancer activity or are known to decrease PSA.