This is a study to determine the recommended dose of MK-8628 (formerly known as OTX015) for further studies in participants with advanced nuclear protein in testis (NUT) midline carcinoma (NMC), triple negative breast cancer (TNBC), non-small cell lung cancer (NSCLC), or castration-resistant prostate cancer (CRPC). This is a two-part parallel study: Part A will establish the recommended dose by evaluating dose limiting toxicity (DLT), safety, discontinuation, and early efficacy and Part B will enroll participants with NMC only and will evaluate safety and efficacy in this population.