• PHASE 1, PHASE 2, AND 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 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, PHASE 2, AND 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 and Phase 2.

• PHASE 1, PHASE 2, AND 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, PHASE 2, AND 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, PHASE 2, AND 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, PHASE 2, AND NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Ability to swallow and retain oral medications.

• PHASE 1, PHASE 2, AND NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Absolute neutrophil count \>= 1.5 x 10\^9/L

• PHASE 1, PHASE 2, AND NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Platelets \>= 125 x 10\^9/L

• PHASE 1, PHASE 2, AND NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Hemoglobin \>= 9.0 g/dL

• PHASE 1, PHASE 2, AND NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Albumin \>= 2.5 g/dL

• PHASE 1, PHASE 2, AND NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) for age

• PHASE 1, PHASE 2, AND 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, PHASE 2, AND 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, PHASE 2, AND NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Prothrombin time (PT)/international normalized ratio (INR) =\< 1.5 x ULN

• PHASE 1, PHASE 2, AND NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Partial thromboplastin time (PTT) =\< 1.5 x ULN

• PHASE 1, PHASE 2, AND 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, PHASE 2, AND 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, PHASE 2, AND 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, PHASE 2, AND 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, PHASE 2, AND 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 phase 2 or non-thoracic, non-BRD4 exploratory cohort. Participants enrolling to the phase 2 or 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, PHASE 2, AND 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, PHASE 2, AND 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, PHASE 2, AND 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, PHASE 2, AND NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Women of childbearing potential must have a negative pregnancy test within 7 days of starting treatment.

• PHASE 1, PHASE 2, AND 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. There is no required washout for previous EP therapy.

• PHASE 1, PHASE 2, AND NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Participants may have had a maximum of 2 prior cycles of EP (cisplatin + etoposide). However, for consistency, cycle 1 day 1 will be the first day of EP on the Phase 1 and 2 portions of the study. There is no required washout for previous ZEN003694 therapy for patients enrolling to the phase 1 or phase 2 portion of the study.

• PHASE 1, PHASE 2, AND 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, PHASE 2, AND NON-THORACIC, NON-BRD4 EXPLORATORY COHORT: Participants who have had major surgery can be enrolled at least 3 weeks after the surgery.

• PHASE 1, PHASE 2, AND 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 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 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).