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 oral medications
* Absolute neutrophil count \>= 1.5 x 10\^9/L
* Platelets \>= 100 x 10\^9/L
* Hemoglobin \>= 9.0 g/dL
* Albumin \>= 2.5 g/dL
* Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) for age
* Aspartate aminotransferase (AST)(serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT)(serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN for age OR
* Calculated creatinine clearance \>= 60 mL/min (via the using CKD-epi equation)
* Prothrombin time (PT)/international normalized ratio (INR) =\< 1.5 x ULN
* Partial thromboplastin time (PTT) =\< 1.5 x ULN
* Left ventricular ejection fraction \>= lower limit of normal (LLN)
* Troponin T =\< ULN
* 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
* For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated
* 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
* 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 phase 2 or non-BRD4 exploratory cohort
* The effects of GSK525762C 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) from the time of the screening, for the duration of study participation, and for 7 months after the completion of GSK525762C administration. 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 GSK525762C administration.

  * For female subjects of child-bearing potential receiving GSK525762C, all hormonal means of birth control 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%. Defined as:

      * Intrauterine device (IUD) or intrauterine system (IUS) that meets the \< 1% failure rate as stated in the product label
    * Note: Hormonal IUDs 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 when taking GSK525762C
      * 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
* 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
* Ability to understand and the willingness to sign a written informed consent document (or parent or legally authorized representative, if minor)
* Women of childbearing potential must have a negative pregnancy test within 7 days of starting treatment
* 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. There is no required washout for previous EP therapy. There is no required washout for previous GSK525762C therapy for patients enrolling to the dose escalation or phase 2 portion of the study
* Participants who have received prior radiation therapy can be enrolled at least 1 week after completing radiation
* Participants who have had major surgery can be enrolled at least 3 weeks after the surgery
* Any therapy-related toxicities must have resolved to =\< grade 1 or baseline as per the judgement of the treating investigator (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 GSK525762C. Toxicities attributed to current EP therapy are excluded from this requirement for participants enrolling to the dose escalation or phase 2 portion of the study, as long as the participant meets all other eligibility criteria
* NON-THORACIC,NON-BRD4 EXPLORATORY COHORT
* Participants must lack BRD4-NUT rearrangement as identified via FISH testing performed at the BWH CAMD

Exclusion Criteria:

* PHASE 1, PHASE 2, AND NON-THORACIC,NON-BRD4 EXPLORATORY COHORT.
* Participants with known untreated central nervous system (CNS) metastases. Patients with a history of CNS metastases are eligible, provided they meet the following criteria:

  * 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
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to the study agent(s) (e.g., benzodiazepines for GSK525762C) the participant will be receiving once enrolled
* 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
* Any gastrointestinal (GI) disorder that may affect absorption of oral medications in the opinion of the treating investigator, such as malabsorption syndrome or major bowel or stomach resection
* Fridericia's correction formula (QTcF) \> 450 msec on screening electrocardiogram (ECG)
* Patients who are receiving any other investigational agents
* GSK525762C is primarily metabolized by CYP3A4; therefore, concomitant administration with strong inhibitors or inducers of CYP3A4 should be avoided unless medically necessary. 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
* Pregnant women are excluded from this study because GSK525762C is a 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 GSK525762C, breastfeeding should be discontinued if the mother is treated with GSK525762C. These potential risks may also apply to other agents used in this study
* Patients receiving therapeutic-dose anticoagulation (e.g., warfarin, low-molecular weight heparin \[LMWH\], or novel oral anticoagulants) are not eligible. Prophylactic anticoagulation, with low doses (per standard practice) of agents such as low molecular weight heparin (LMWH), direct thrombin inhibitors, or factor Xa inhibitors are permitted
* Patients who are known to require concurrent use of nonsteroidal antiinflammatory drugs (NSAIDS), except for cases where NSAIDS provide benefit over other analgesics or high dose aspirin (patients are allowed up to 100 mg aspirin PO daily)
* Patients with a history of known bleeding disorders or history of clinically significant hemorrhage (e.g. GI, neurologic) within the past 6 months
* Cardiac abnormalities as evidenced by any of the following:

  * Clinically significant conduction abnormalities or arrhythmias. NOTE: Any clinically significant ECG assessments should be reviewed by the site cardiologist prior to study entry
  * Presence of cardiac pacemaker or defibrillator with a paced ventricular rhythm limiting ECG analysis
  * 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 OR PHASE 2
* For enrollment to the dose escalation or phase 2 portion of the study: patients who are currently receiving EP or GSK525762C, or received EP or GSK525762C 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 GSK525762C due to unacceptable toxicities attributed to the agent(s) are not eligible
* Patients must be candidates to receive EP per institutional standards of practice and/or the Food and Drug Administration (FDA) package inserts as judged by the treating investigator
* NON-THORACIC, NON-BRD4 EXPLORATORY COHORT
* For enrollment to the non-BRD4 exploratory cohort: patients who previously received treatment with a BETi, including but not limited to previous GSK525762C therapy. Exceptions may be allowed for patients who have not received treatment with GSK525762C but who have received a different BETi with approval from the overall principal investigator
* For enrollment to the non-BRD4 exploratory cohort: patients with disease that 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 with approval from the overall principal investigator