Inclusion Criteria:

          -  Patients must have measurable disease, defined as at least one lesion that can be
             accurately measured in at least one dimension (longest diameter to be recorded for
             non-nodal lesions and short axis for nodal lesions) as >= 20 mm (>= 2 cm) with
             conventional techniques or as >= 10 mm (>= 1 cm) with spiral computed tomography (CT)
             scan, magnetic resonance imaging (MRI), or calipers by clinical exam; baseline imaging
             must be obtained within 30 days of day 1 of study

          -  Patients must have histologically confirmed epithelioid hemangioendothelioma which is
             metastatic or locally advanced (unresectable), and tumor tissue (paraffin-embedded
             tissue block or tumor tissue on unstained glass slides) available for fusion
             fluorescence in situ hybridization (FISH) analysis at Cleveland Clinic; patient tumor
             tissue stored in pathology archives may be used for fusion FISH; a new biopsy is not
             mandatory

          -  Patients must have evidence of disease progression per RECIST 1.1 prior to enrollment
             or have evidence of cancer-related pain requiring symptom management with narcotic
             analgesics

          -  Because there is no established standard or approved drug therapy for treatment of
             epithelioid hemangioendothelioma (EHE), patients previously untreated or treated with
             drug therapy for EHE are eligible; there is no limit on the number of prior regimens
             used to be eligible

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky >= 60%)

          -  Life expectancy of greater than 6 months

          -  Able to swallow orally-administered medication and does not have any clinically
             significant gastrointestinal abnormalities that may alter absorption such as
             malabsorption syndrome or major resection of the stomach or small bowel

          -  All prior treatment-related toxicities must be Common Terminology Criteria for Adverse
             Events version 5.0 (CTCAE v5) grade =< 1 (except alopecia) at the time of enrollment

          -  Absolute neutrophil count (ANC) >= 1 x 10^9/L (within 2 weeks of patient registration)

          -  Hemoglobin >= 9 g/dL, patients may receive transfusion to meet criterion (within 2
             weeks of patient registration)

          -  Platelets >= 75 x 10^9/L (within 2 weeks of patient registration)

          -  Albumin >= 2.5 g/dL (within 2 weeks of patient registration)

          -  Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) (within 2 weeks of
             patient registration); NOTE: patients with elevated bilirubin secondary to Gilbert's
             disease are eligible to participate in the study

          -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 2.5 x
             institutional ULN (within 2 weeks of patient registration)

          -  Serum creatinine =< 1.5 mg/dL OR calculated creatinine clearance (Cockcroft-Gault
             formula) >= 50 mL/min OR 24-hour urine creatinine clearance >= 50 mL/min (within 2
             weeks of patient registration)

          -  Left ventricular ejection fraction (LVEF) >= institutional lower limit of normal (LLN)
             by echocardiogram (ECHO) or multigated acquisition scan (MUGA) (within 30 days of
             registration)

          -  Trametinib can cause fetal harm when administered to a pregnant woman; women of
             child-bearing potential and men must agree to use adequate contraception (hormonal or
             barrier method of birth control; abstinence) prior to study entry, during the study
             participation, and for four months after the last dose of the drug; women of
             child-bearing potential must have a negative serum pregnancy test within 14 days prior
             to enrollment and agree to use effective contraception throughout the treatment period
             and for 4 months after the last dose of study treatment; 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

          -  Human immunodeficiency virus (HIV)-patients positive for human immunodeficiency virus
             (HIV) are NOT excluded from this study, however HIV-positive patients must meet the
             following criteria:

               -  A stable regimen of highly active anti-retroviral therapy (HAART)

               -  No requirement for concurrent antibiotics or antifungal agents for the prevention
                  of opportunistic infections

               -  A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard
                  polymerase chain reaction (PCR)-based test

        Exclusion Criteria:

          -  Prior systemic therapy with a MEK inhibitor

          -  History of another malignancy

               -  Exception: patients who have been disease-free for 3 years or patients with a
                  history of completely resected non-melanoma skin cancer and/or patients with
                  indolent secondary malignancies, are eligible; consult the Cancer Therapy
                  Evaluation Program (CTEP) medical monitor if unsure whether second malignancies
                  meet the requirements specified above

          -  History of interstitial lung disease or pneumonitis requiring supplemental oxygen or
             treatment with oral or intravenously administered corticosteroids

          -  Any major surgery, extensive radiotherapy, chemotherapy with delayed toxicity (e.g.
             doxorubicin), biologic therapy, or immunotherapy within 21 days prior to enrollment
             and/or daily or weekly chemotherapy (e.g. sunitinib, sorafenib and pazopanib) without
             the potential for delayed toxicity within 14 days prior to enrollment

          -  Use of other investigational drugs within 28 days (or five half-lives, whichever is
             shorter; with a minimum of 14 days from the last dose) preceding the first dose of
             trametinib and during the study

          -  Symptomatic or untreated leptomeningeal or brain metastases or spinal cord compression

          -  Have a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs
             chemically related to trametinib, or excipients or to dimethyl sulfoxide (DMSO)

          -  Current use of a prohibited medication; the following medications or non-drug
             therapies are prohibited:

               -  Other anti-cancer therapy while on study treatment; (note: megestrol [Megace] if
                  used as an appetite stimulant is allowed)

               -  Concurrent treatment with bisphosphonates is permitted; however, treatment must
                  be initiated prior to the first dose of study therapy; prophylactic use of
                  bisphosphonates in patients without bone disease is not permitted, except for the
                  treatment of osteoporosis

               -  Because the composition, pharmacokinetics (PK), and metabolism of many herbal
                  supplements are unknown, the concurrent use of all herbal supplements is
                  prohibited during the study (including, but not limited to, St. John's wort,
                  kava, ephedra [ma huang], ginkgo biloba, dehydroepiandrosterone [DHEA], yohimbe,
                  saw palmetto, or ginseng)

          -  History or current evidence/risk of retinal vein occlusion (RVO)

          -  History or evidence of cardiovascular risk including any of the following:

               -  A QT interval corrected for heart rate using the Bazett's formula QTcB >= 480
                  msec

               -  History or evidence of current clinically significant uncontrolled arrhythmias
                  (exception: patients with controlled atrial fibrillation for > 30 days prior to
                  randomization are eligible)

               -  History of acute coronary syndromes (including myocardial infarction and unstable
                  angina), coronary angioplasty, or stenting within 6 months prior to randomization

               -  History or evidence of current >= class II congestive heart failure as defined by
                  the New York Heart Association (NYHA) functional classification system

               -  Treatment-refractory hypertension defined as a blood pressure of systolic > 140
                  mmHg and/or diastolic > 90 mmHg which cannot be controlled by anti-hypertensive
                  therapy

               -  Patients with intra-cardiac defibrillators

               -  Known cardiac metastases

          -  Known hepatitis B virus (HBV), or hepatitis C virus (HCV) infection (patients with
             chronic or cleared HBV and HCV infection are eligible)

          -  Any serious and/or unstable pre-existing medical disorder (aside from malignancy
             exception above), psychiatric disorder, or other conditions that could interfere with
             subject's safety, obtaining informed consent or compliance to the study procedures

          -  Trametinib was embryotoxic and abortifacient in rabbits at doses greater than or equal
             to those resulting in exposures approximately 0.3 times the human exposure at the
             recommended clinical dose. Therefore, the study drug must not be administered to
             pregnant women or nursing mothers; women of childbearing potential should be advised
             to avoid pregnancy and use effective methods of contraception; men with a female
             partner of childbearing potential must have either had a prior vasectomy or agree to
             use effective contraception; if a female patient or a female partner of a patient
             becomes pregnant while the patient receives trametinib, the potential hazard to the
             fetus should be explained to the patient and partner (as applicable)

          -  Inability to comply with protocol-required procedures