Testing of the Addition of a New Anti-cancer Drug, Molibresib, to Chemotherapy Treatment (Etoposide and Cisplatin) for Patients With NUT Carcinoma

Inclusion Criteria: * PHASE 1, PHASE 2, AND NON-THORACIC, NON-BRD4 EXPLORATORY COHORT * Patients must have histologically or cytologically confirmed NUT carcinoma (NC) based on at least one of the following criteria: * Ectopic expression of NUT protein (\> 50% tumor nuclei) as determined by immunohistochemistry (IHC) testing performed in a Clinical Laboratory Improvement Act (CLIA) certified laboratory * Detection of the NUT gene translocation as determined by fluorescence in situ hybridization (FISH) performed at the Brigham and Women's Hospital (BWH) Center for Advanced Molecular Diagnostics (CAMD) * Participants must have disease that is metastatic, unresectable, or for which a surgical approach would not likely confer a survival benefit or would be otherwise contraindicated in the opinion of the treating investigator. Participants who have already undergone surgical resection are eligible * Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 (Karnofsky \>= 60%) for patients \>= 16 years of age, Lansky \>= 50% if \< 16 years of age * Participants must have measurable disease per RECIST version 1.1 criteria. Participants enrolling to the phase 1 or non-BRD4 exploratory cohort without measurable disease per the RECIST definition may be allowed to enroll with permission from the overall principal investigator if their disease is otherwise evaluable (e.g. bone metastases, malignant pleural effusions, malignant ascites * Ability to swallow and retain ora…