Tazemetostat in Treating Patients With Relapsed or Refractory Advanced Solid Tumors, Non-Hodgkin Lymphoma, or Histiocytic Disorders With EZH2, SMARCB1, or SMARCA4 Gene Mutations (A Pediatric MATCH Treatment Trial)

Inclusion Criteria:

* Patient must have enrolled onto APEC1621SC and must have been given a treatment assignment to Molecular Analysis for Therapy Choice (MATCH) to APEC1621C based on the presence of an actionable mutation
* Patients must have radiographically measurable disease at the time of study enrollment; patients with neuroblastoma who do not have measurable disease but have MIBG+ evaluable disease are eligible; measurable disease in patients with CNS involvement is defined as tumor that is measurable in two perpendicular diameters on magnetic resonance imaging (MRI) and visible on more than one slice; Note: The following do not qualify as measurable disease:

  * Malignant fluid collections (e.g., ascites, pleural effusions)
  * Bone marrow infiltration except that detected by MIBG scan for neuroblastoma
  * Lesions only detected by nuclear medicine studies (e.g., bone, gallium or positron emission tomography \[PET\] scans) except as noted for neuroblastoma
  * Elevated tumor markers in plasma or cerebrospinal fluid (CSF)
  * Previously radiated lesions that have not demonstrated clear progression post radiation
  * Leptomeningeal lesions that do not meet the measurement requirements for Response Evaluation Criteria in Solid Tumors (RECIST) 1.1
* Karnofsky \>= 50% for patients \> 16 years of age and Lansky \>= 50 for patients =\< 16 years of age; Note: Neurologic deficits in patients with CNS tumors must have been stable for at least 7 days prior to study enrollment; patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score
* Patients must have fully recovered from the acute toxic effects of all prior anti-cancer therapy and must meet the following minimum duration from prior anti-cancer directed therapy prior to enrollment; if after the required timeframe, the numerical eligibility criteria are met, e.g. blood count criteria, the patient is considered to have recovered adequately

  * Cytotoxic chemotherapy or other anti-cancer agents known to be myelosuppressive

    * \>= 21 days after the last dose of cytotoxic or myelosuppressive chemotherapy (42 days if prior nitrosourea)
  * Anti-cancer agents not known to be myelosuppressive (e.g. not associated with reduced platelet or absolute neutrophil count \[ANC\] counts): \>= 7 days after the last dose of agent
  * Antibodies: \>= 21 days must have elapsed from infusion of last dose of antibody, and toxicity related to prior antibody therapy must be recovered to grade =\< 1
  * Corticosteroids: If used to modify immune adverse events related to prior therapy, \>= 14 days must have elapsed since last dose of corticosteroid
  * Hematopoietic growth factors: \>= 14 days after the last dose of a long-acting growth factor (e.g. pegfilgrastim) or 7 days for short-acting growth factor; for growth factors that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur; the duration of this interval must be discussed with the study chair and the study-assigned research coordinator
  * Interleukins, interferons and cytokines (other than hematopoietic growth factors): \>= 21 days after the completion of interleukins, interferon or cytokines (other than hematopoietic growth factors)
  * Stem cell Infusions (with or without total body irradiation \[TBI\]):

    * Allogeneic (non-autologous) bone marrow or stem cell transplant, or any stem cell infusion including donor lymphocyte infusion (DLI) or boost infusion: \>= 84 days after infusion and no evidence of graft versus host disease (GVHD)
    * Autologous stem cell infusion including boost infusion: \>= 42 days
  * Cellular therapy: \>= 42 days after the completion of any type of cellular therapy (e.g. modified T cells, natural killer \[NK\] cells, dendritic cells, etc.)
  * Radiation therapy (XRT)/external beam irradiation including protons: \>= 14 days after local XRT; \>= 150 days after TBI, craniospinal XRT or if radiation to \>= 50% of the pelvis; \>= 42 days if other substantial bone marrow (BM) radiation; Note: Radiation may not be delivered to "measurable disease" tumor site(s) being used to follow response to subprotocol treatment
  * Radiopharmaceutical therapy (e.g., radiolabeled antibody, 131I-MIBG): \>= 42 days after systemically administered radiopharmaceutical therapy
  * Patients must not have had prior exposure to tazemetostat or other inhibitor(s) of EZH2
* For patients with solid tumors without known bone marrow involvement:

  * Peripheral absolute neutrophil count (ANC) \>= 1000/mm\^3
  * Platelet count \>= 100,000/mm\^3 (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment)
  * Hemoglobin \>= 8.0 g/dL at baseline (may receive red blood cell \[RBC\] transfusions)
* Patients with known bone marrow metastatic disease will be eligible for study provided they meet the blood counts (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these patients will not be evaluable for hematologic toxicity
* Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 ml/min/1.73 m\^2 or a serum creatinine based on age/gender as follows:

  * Age 1 to \< 2 years: male: 0.6 mg/dL; female: 0.6 mg/dL
  * Age 2 to \< 6 years: male: 0.8 mg/dL; female: 0.8 mg/dL
  * Age 6 to \< 10 years: male: 1 mg/dL; female: 1 mg/dL
  * Age 10 to \< 13 years: male: 1.2 mg/dL; female: 1.2 mg/dL
  * Age 13 to \< 16 years: male: 1.5 mg/dL; female: 1.4 mg/dL
  * Age \>= 16 years: male: 1.7 mg/dL; female: 1.4 mg/dL
* Bilirubin (sum of conjugated + unconjugated) =\< 1.5 x upper limit of normal (ULN) for age
* Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 135 U/L; (for the purpose of this study, the ULN for SGPT is 45 U/L)
* Serum albumin \>= 2 g/dL
* Corrected QT (QTc) interval =\< 480 milliseconds
* Patients with seizure disorder may be enrolled if on anticonvulsants and well controlled
* Nervous system disorders (Common Terminology Criteria for Adverse Events \[CTCAE\] version \[V\] 4.0) resulting from prior therapy must be =\< grade 2, with the exception of decreased tendon reflex (DTR). Any grade of DTR is eligible
* International normalized ratio (INR) =\< 1.5
* For subjects with CNS involvement (primary tumor or metastatic disease): Subjects must not have any active bleeding, or new intratumoral hemorrhage of more than punctate size on screening MRI or known bleeding diathesis or treatment with anti-platelet or anti-thrombotic agents
* All patients and/or their parents or legally authorized representatives must sign a written informed consent; assent, when appropriate, will be obtained according to institutional guidelines

Exclusion Criteria:

* Pregnant or breast-feeding women will not be entered on this study because there is currently no available information regarding human fetal or teratogenic toxicities; pregnancy tests must be obtained in girls who are post-menarchal; males or females of reproductive potential may not participate unless they have agreed to use an effective contraceptive method for the duration of study treatment; female subjects of childbearing potential should agree to remain abstinent or use adequate contraceptive methods for 30 days after the last dose of tazemetostat; male subjects should agree to remain abstinent or use adequate contraceptive methods, and agree to refrain from donating sperm, and for 90 days after the last dose of tazemetostat
* Patients receiving corticosteroids who have not been on a stable or decreasing dose of corticosteroid for at least 7 days prior to enrollment are not eligible; if used to modify immune adverse events related to prior therapy, \>= 14 days must have elapsed since last dose of corticosteroid
* Patients who are currently receiving another investigational drug are not eligible
* Patients who are currently receiving other anti-cancer agents are not eligible
* Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial
* Patients who are currently receiving drugs that are strong inducers or strong inhibitors of CYP3A4 are not eligible; strong inducers or inhibitors of CYP3A4 are prohibited from 14 days prior to the first dose of tazemetostat to the end of the study; Note: Dexamethasone for CNS tumors or metastases, on a stable dose, is allowed
* Patients who have an uncontrolled infection are not eligible
* On complete blood count (CBC) differential, patients must not have any significant morphologic abnormalities concerning for myeloproliferative neoplasm (MPN)/myelodysplastic syndrome (MDS) or T- acute lymphoblastic leukemia (ALL)
* Patients must not have thrombocytopenia, neutropenia, or anemia of grade \>= 3 (per CTCAE 5.0 criteria) or any prior history of myeloid malignancies, including myelodysplastic syndrome (MDS)
* Patients with a history of prior history of T-lymphoblastic lymphoma (LBL)/T-ALL
* Patients with any prior history of myeloid malignancies, including myelodysplastic syndrome (MDS).
* Patients who have received prior solid organ transplantation are not eligible
* Patients who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study are not eligible