Testing the Safety and Efficacy of the Addition of a New Anti-cancer Drug, ZEN003694, to Chemotherapy Treatment (Cisplatin and Etoposide or Carboplatin and Paclitaxel) for Adult and Pediatric Patients (12-17 Years) With NUT Carcinoma

Inclusion Criteria: * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Participants must have a diagnosis of NC based on standard criteria for the disease, with diagnostic testing performed in a Clinical Laboratory Improvement Act (CLIA) certified laboratory: * Ectopic expression of NUT protein per World Health Organization (WHO) criteria (World Health Organization \[WHO\], 2021) as determined by immunohistochemistry (IHC) testing, OR * Detection of the NUT gene translocation as determined by fluorescence in situ hybridization (FISH) testing, OR * Detection of the NUT gene translocation as determined by sequencing, eg. DNA next generation sequencing (NGS) or RNA sequencing. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: 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. Participants who have already undergone surgical resection are eligible to participate in Phase 1. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Age \>= 12 years. Patients 12-17 years of age must be \>= 40 kg at enrollment. Because no dosing or adverse event data are currently available on the use of ZEN003694 in combination with etoposide and cisplatin in patients \< 12 years of age, younger children are excluded from this study. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 (Karnofsky \>= 60%) for patients \>= 16 years of age, Lansky \>= 50% if \< 16 years of age. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Participants must have measurable disease per RECIST version 1.1 criteria. Patients in the phase 1 portion do not need measurable disease if their disease is otherwise evaluable. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Ability to swallow and retain oral medications. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Absolute neutrophil count \>= 1.5 x 10\^9/L. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Platelets \>= 125 x 10\^9/L. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Hemoglobin \>= 9.0 g/dL. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Albumin \>= 2.5 g/dL. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) for age. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Aspartate aminotransferase (AST)(serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase(ALT)(serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN for age. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Calculated creatinine clearance \>= 60 mL/min (based on the calculated Chronic Kidney Disease Epidemiology Collaboration \[CKD-EPI\] glomerular filtration rate estimation for adults or 60 mL/min/1.73m\^2 for patients 12-17 years as calculated based on bedside Schwartz formula). * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Prothrombin time (PT)/international normalized ratio (INR) =\< 1.5 x ULN. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Partial thromboplastin time (PTT) =\< 1.5 x ULN. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: QT interval by Fridericia (QTcF) \< 450 ms (machine or manual read allowed). Patients should avoid medications which prolong the QT. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 3 months are eligible for this trial as long as their anti-retroviral therapy does not have the potential for drug-drug interactions as judged by the treating investigator. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. Hepatitis C (HepC antibody) testing is required. Hepatitis C RNA is optional; however, a confirmatory negative hepatitis C RNA test must be obtained to be able to enroll participants with positive hepatitis C antibody due to prior resolved disease. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for treatment in the phase 1 portion, but not in the non-thoracic, non-BRD4 exploratory cohort. Participants enrolling to the non-thoracic, non-BRD4 exploratory cohort with a history of prior malignancy are eligible only if they fit one or more of the following criteria: participants with non-melanoma skin cancers that have been curatively treated; participants with adequately treated carcinomas in situ of any type; or participants who were diagnosed and curatively treated at least 3 years prior to the date of study entry and who are considered by the treating investigator to be at low risk for recurrence. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: The effects of ZEN003694 on the developing human fetus are unknown. For this reason and because the chemotherapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (barrier method of birth control; abstinence) prior to study entry and for the duration of study participation and for 4 months after completion of study therapy. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of study therapy. For female subjects of child-bearing potentially receiving ZEN003694, hormonal means of birth control alone, such as oral, injectable, dermal, subdermal or topical contraceptives are NOT acceptable forms of birth control given that their efficacy has not been evaluated when given in combination with the investigational drugs. "Adequate contraception" is defined as the following: Contraceptive methods with a failure rate of =\< 1% used in combination with the barrier method. The following contraceptive methods are acceptable to use in combination with the barrier method: intrauterine device (IUD), intrauterine system (IUS), or oral contraceptive pills (OCPs) that meet the \< 1% failure rate as stated in the product label. Note: Hormonal IUDs/OCPs may only be used if the following criteria are met: male condoms are required AND subjects are informed of the potential for reduced systemic hormone levels from the IUD/OCP when taking ZEN003694. Alternatively, male partner sterilization (vasectomy with documentation of azoospermia) prior to the female subject's entry into the study, and this male is the sole partner for that subject. For this definition, "documented" refers to the outcome of the investigator's/designee's medical examination of the subject or review of the subject's medical history for study eligibility, as obtained via a verbal interview with the subject or from the subject's medical records. Male subjects with female partners of child-bearing potential must use one of the following contraceptive methods: * Vasectomy with documentation of azoospermia OR * Condom use PLUS partner use of a highly effective contraceptive (=\< 1% rate of failure per year) such as intrauterine device or system, or hormonal birth control such as contraceptive subdermal implant, combined estrogen and progestogen oral contraceptive, injectable progestogen, contraceptive vaginal ring, or percutaneous contraceptive patches. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Male subjects should not donate sperm while on study and for 16 weeks after the last dose of study medication. Male subjects whose partners are or become pregnant must continue to use condoms for 16 weeks after the last dose of study medication. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Ability to understand and the willingness to sign a written informed consent document (or parent or legally authorized representative if minor). Participants with impaired decision-making capacity (IDMC) who have a legally-authorized representative (LAR) and/or family member available may be eligible after discussion with the Principal Investigator of this study. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Women of childbearing potential must have a negative pregnancy test within 7 days of starting treatment. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Participants who have not had cytotoxic chemotherapy, oral tyrosine kinase inhibitor (TKI) or small molecule therapy, or immunotherapy within 2 weeks prior to the first dose of study medication or 5 half-lives, whichever is shorter. For the phase 1 dose escalation, there is no required washout for previous EP therapy. For the carboplatin/paclitaxel safety cohort, there is no required washout for prior carboplatin/paclitaxel therapy * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Participants may have had a maximum of 1 prior cycle of EP (cisplatin + etoposide) or carboplatin/paclitaxel. However, for consistency, cycle 1 day 1 will be the first day of EP or carboplatin/paclitaxel on the Phase 1 portions of the study. There is no required washout for previous ZEN003694 therapy for patients enrolling to the phase 1 portion of the study * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Participants who have received prior radiation therapy can be enrolled at least 1 week after completing radiation. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Participants who have had major surgery can be enrolled at least 3 weeks after the surgery. * PHASE 1, CARBOPLATIN/PACLITAXEL SAFETY COHORT, \& NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Any therapy-related toxicities must have resolved to ≤ grade 1 or baseline (with the exception of alopecia, peripheral neuropathy, or rash that will be permitted at ≤ grade 2). Other grade 2 toxicities attributed to prior treatment may be permitted with agreement from the overall principal investigator if they are toxicities not commonly attributed to ZEN003694. Toxicities attributed to current EP or carboplatin/paclitaxel therapy are excluded from this requirement for participants enrolling to the dose escalation or carboplatin/paclitaxel safety cohort, as long as the participant meets all other eligibility criteria. * NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Participants must have a diagnosis of NC but lack BRD4-NUT rearrangement. If the fusion status is unknown after NC diagnosis, the BRD4-NUT fusion status will be determined by centralized FISH testing at the BWH Center for Advanced Molecular Diagnostics (CAMD). Exclusion Criteria: * PHASE 1, NON-THORACIC, NON-BRD4 EXPLORATORY COHORT, \& CARBOPLATIN/PACLITAXEL SAFETY COHORT: Participants with known untreated central nervous system (CNS) metastases. Patients with a history of treated CNS metastases are eligible, provided they meet the following criteria: * Radiologically stable for 4 weeks. * Disease outside the CNS is present. * Recovery from acute toxicity associated with the treatment to =\< Common Terminology Criteria for Adverse Events (CTCAE) grade 1 or baseline (with the exception of alopecia), with no requirement for escalating doses of corticosteroids over the past 7 days. * Subjects currently taking enzyme-inducing anticonvulsants (EIAC) must be transitioned to non-enzyme inducing anticonvulsants at least 14 days or 5 half-lives prior to the first dose of study medication * No presence of symptomatic or untreated leptomeningeal metastases or spinal cord compression. * PHASE 1, NON-THORACIC, NON-BRD4 EXPLORATORY COHORT, \& CARBOPLATIN/PACLITAXEL SAFETY COHORT: History of allergic reactions attributed to compounds of similar chemical or biologic composition to ZEN003694 or other agents used in study. * PHASE 1, NON-THORACIC, NON-BRD4 EXPLORATORY COHORT, \& CARBOPLATIN/PACLITAXEL SAFETY COHORT: Uncontrolled intercurrent illness including, but not limited to: ongoing or active infection requiring systemic treatment, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. Patients with myocardial infarction or unstable angina within 6 months prior to the first dose of ZEN003694 will be excluded. * PHASE 1, NON-THORACIC, NON-BRD4 EXPLORATORY COHORT, \& CARBOPLATIN/PACLITAXEL SAFETY COHORT: Any gastrointestinal (GI) disorder that may affect absorption of ZEN003694 and other oral medications in the opinion of the treating investigator, such as malabsorption syndrome or major bowel or stomach resection. * PHASE 1, NON-THORACIC, NON-BRD4 EXPLORATORY COHORT, \& CARBOPLATIN/PACLITAXEL SAFETY COHORT: Patients who are receiving any other investigational agents. * PHASE 1, NON-THORACIC, NON-BRD4 EXPLORATORY COHORT, \& CARBOPLATIN/PACLITAXEL SAFETY COHORT: Patients receiving any medications or substances that are strong inhibitors or inducers of CYP3A4 or substrates of CYP1A2 with narrow therapeutic windows are ineligible. Strong inhibitors or inducers of CYP3A4 must be discontinued at least 7 days prior to the first dose of ZEN003694. As proton pump inhibitors (PPIs), H2 receptor antagonists, and antacids may alter the pharmacokinetics of ZEN003694 by reducing ZEN003694 exposure, patients receiving proton pump inhibitors are ineligible. If H2 blockers or other acid reducing agents are used concomitantly with ZEN003694, a staggered dosing schedule should be used, either dose ZEN-3694 2 hours before the H2 blocker or 10-12 hours after an H2 blocker. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product. * PHASE 1, NON-THORACIC, NON-BRD4 EXPLORATORY COHORT, \& CARBOPLATIN/PACLITAXEL SAFETY COHORT: Pregnant women are excluded from this study because ZEN003694 is a bromodomain and extraterminal domain (BET) inhibitor with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with ZEN003694, breastfeeding should be discontinued if the mother is treated with ZEN003694. These potential risks may also apply to other agents used in this study. * PHASE 1, NON-THORACIC, NON-BRD4 EXPLORATORY COHORT, \& CARBOPLATIN/PACLITAXEL SAFETY COHORT: Patients receiving therapeutic-dose anticoagulation (e.g., warfarin, low-molecular weight heparin \[LMWH\], or novel oral anticoagulants) are not eligible. Use of oral Factor Xa inhibitors (i.e., rivaroxaban, apixaban, betrixaban, edoxaban otamixaban, letaxaban, eribaxaban) and Factor IIa inhibitors (i.e., dabigatran) is not permitted. Prophylactic anticoagulation, with low doses (per standard practice) of agents such as low molecular weight heparin (LMWH) is permitted. * PHASE 1, NON-THORACIC, NON-BRD4 EXPLORATORY COHORT, \& CARBOPLATIN/PACLITAXEL SAFETY COHORT: Patients with radiation to \> 25% of the bone marrow. * PHASE 1, NON-THORACIC, NON-BRD4 EXPLORATORY COHORT, \& CARBOPLATIN/PACLITAXEL SAFETY COHORT: Cardiac abnormalities as evidenced by any of the following: * Clinically significant conduction abnormalities or arrhythmias. * History or evidence of current \>= class II congestive heart failure as defined by New York Heart Association (NYHA). * History of acute coronary syndromes (including unstable angina and myocardial infarction), coronary angioplasty, or stenting within the past 3 months. Subjects with a history of stent placement requiring ongoing antithrombotic therapy (e.g., clopidogrel, prasugrel) will not be permitted to enroll. * Clinically significant cardiomegaly, ventricular hypertrophy, or cardiomyopathy. * PHASE 1, NON-THORACIC, NON-BRD4 EXPLORATORY COHORT, \& CARBOPLATIN/PACLITAXEL SAFETY COHORT: Patients with uncontrolled intercurrent illness. * PHASE 1, NON-THORACIC, NON-BRD4 EXPLORATORY COHORT, \& CARBOPLATIN/PACLITAXEL SAFETY COHORT: Patients with psychiatric illness/social situations that would limit compliance with study requirements. * PHASE 1: Patients who are currently receiving EP or ZEN003694, or received EP or ZEN003694 in the past, must be candidates to receive the study agents at the protocol-defined dose level and schedule as judged by the treating investigator. Patients who previously required dose reductions of their EP or ZEN003694 due to unacceptable toxicities attributed to the agent(s) are not eligible. * ZEN003694/CARBOPLATIN/PACLITAXEL SAFETY COHORT: Patients who are currently receiving carboplatin/paclitaxel or ZEN003694, or received carboplatin/paclitaxel or ZEN003694 in the past, must be candidates to receive the study agents at the protocol-defined dose level and schedule as judged by the treating investigator. Patients who previously required dose reductions of their carboplatin/paclitaxel or ZEN003694 due to unacceptable toxicities attributed to the agent(s) are not eligible. * PHASE 1 OR ZEN003694/CARBOPLATIN/PACLITAXEL SAFETY COHORT: Patients ineligible for receiving EP or carboplatin/paclitaxel for either the phase 1 dose escalation or the carboplatin/paclitaxel safety cohort, respectively. * NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Patients with disease that definitively originated in the thoracic cavity. In the case of patients with metastatic disease at diagnosis where disease origin is uncertain, the patient may be allowed to enroll. * NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Patients who previously received treatment with a BET inhibitor (BETi), including but not limited to previous ZEN003694 therapy.