Cobimetinib in Refractory Langerhans Cell Histiocytosis (LCH), and Other Histiocytic Disorders

INCLUSION CRITERIA: Age at study entry * For Group 1: Participant must be at least 6 months of age and less than 21 years of age at the time of enrollment * For Group 2: Participant may be at least 6 months of age at the time of enrollment * For Group 3: Participant must be at least 6 months of age and less than 21 years of age at the time of enrollment * For Group 4: Participant must be 21 years of age or older at the time of enrollment * Participant must be able to take an enteral dose and formulation of medication. Study medication is only available as an oral suspension or tablet which may be taken by mouth or other enteral route such as nasogastric or gastric tube. * Biopsy proven LCH -AND * Failure of at least front-line therapy for LCH with evaluable disease. -OR * Diagnosis of LCH-associated neurodegenerative disease with radiologic or clinical progression within the past 3 months. -OR * Biopsy proven JXG, ECD, RDD, histiocytic sarcoma, or other histiocytic lesion (newly diagnosed or relapsed/refractory disease) with evaluable active disease. Performance Level: -Karnofsky ≥ 50% for patients \> 16 years of age and Lansky ≥ 50% for patients ≤ 16 years of age. Adequate Hematologic Function Defined as: * ANC ≥ 0.75 x 10\^9/L (unsupported/without growth factor stimulant) * Platelet count ≥ 75 x 10\^9/L (unsupported/without transfusion within the past 7 days). * Patients with marrow disease must have platelet count of \>/= 75 x 10\^9/L (transfusion support allowed) and must not be refractory to platelet transfusions. * Hemoglobin ≥ 8 g/dL (unsupported/without transfusion within the past 7 days) * Patients with marrow disease must have hemoglobin ≥ 8 g/dL (transfusion support allowed). Adequate Renal Function Defined as: \- Calculated creatinine clearance (or radioisotope GFR) ≥ 70 mL/min/1.73m\^2 or serum creatinine based on age/gender as follows: Maximum Serum Creatinine (mg/dL) Age 2 to \< 6 years: Male 0.8 mg/dL, Female 0.8; 6 to \< 10 years: Male 1 mg/dL,Female 1; 10 to \< 13 years: Male 1.2 mg/dL; Female 1.2; 13 to \< 16 years: Male 1.5 mg/dL ; Female 1.4; ≥ 16 years: Male 1.7 mg/dL; Female 1.4; Adequate Liver Function Defined as: * Bilirubin (sum of conjugated + unconjugated) ≤ 1.5 x upper limit of normal (ULN) for age * AST and ALT ≤ 3x ULN (≤ 5 x ULN for participants with liver involvement) * Serum albumin ≥ 2 g/dL. For patients with liver disease caused by histiocytic disorder: • Patients may be enrolled with abnormal bilirubin, AST, ALT and albumin with documentation of histiocytic liver disease. Adequate Cardiac Function Defined as: \- Fractional shortening (FS) of ≥ 30% or ejection fraction of ≥ 50% by echocardiogram at baseline, as determined by echocardiography or multigated acquisition scan (MUGA) within 28 days prior to enrollment. Depending on institutional standard, either FS or LVEF is adequate for enrollment if only one value is measured; if both values are measured, then both values must meet criteria above Pregnancy/Birth Control * Female patients of childbearing potential require a negative urine or serum pregnancy test for eligibility and again at database registration, if more than 2 weeks has elapsed. * Female patients of childbearing potential must agree to follow the contraceptive requirements using two forms of effective contraceptive methods for the duration of the study treatment. Male patients with sexual partners who are pregnant or who could become pregnant (i.e., women of child-bearing potential) must agree to use two forms of effective methods of contraception (one of which must be a barrier method) during the treatment period and for at least 3 months after the last dose of the study drug to avoid pregnancy and/or potential adverse effects on a developing embryo. Agreement to true abstinence (not periodic abstinence or withdrawal method) is an acceptable method of birth control. EXCLUSION CRITERIA: \- Prior and Concomitant Use of Drugs with CYP3A4 inducing/inhibiting activity: Patient taking strong inducers or inhibitors of CYP3A4 within 14 days prior to study enrollment, including but not limited to the following: erythromycin, clarithromycin, ketoconazole, azithromycin, itraconazole, grapefruit juice or St. John's wort. * Prior Therapy Restrictions Completion of previous chemotherapy, immunotherapy, radiotherapy, or targeted therapy for LCH (or other histiocytic disorder) at least 28 days (except where specified below) prior to study enrollment, with resolution of all associated toxicity to ≤ Grade 1 prior to study enrollment (exception for alopecia and ototoxicity which do not need to be resolved ≤ Grade 1). 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 laboratory eligibility criteria are met, the patient is considered to have recovered adequately. See below for specific consideration of prednisone and corticosteroids prior to enrollment. * Radiation therapy within the 14 days prior to enrollment. * Any prior treatment with Cobimetinib. * Treatment with a long-acting hematopoietic growth factor within 14 days prior to initiation of study drug or a short-acting hematopoietic growth factor within 7 days prior to enrollment. * Treatment with hormonal therapy (except hormone replacement therapy or oral contraceptives), immunotherapy, biologic therapy, investigational therapy, or herbal cancer therapy within 28 days or \< 5 half-lives, whichever is longer, prior to study enrollment. * Treatment with high-dose chemotherapy and stem-cell rescue (autologous stem cell transplant) or allogeneic stem cell transplant within 90 days prior to enrollment. Anti-GVHD agents post-transplant: 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. * For patients with brain tumors (intracranial masses), use of anticoagulants within 7 days prior to enrollment. * Corticosteroid therapy less than or equal to 0.5 mg/kg/day averaged during the 28 days prior to study enrollment is permissible. Patients receiving corticosteroids must be on a stable or decreasing dose for 14 days prior to enrollment and discontinue once study treatment has started. * Patient has received treatment with investigational therapy within 4 weeks prior to initiation of study drug. * Patients taking anticoagulants or have a pre-existing bleeding disorder unrelated to histiocytic disease. * Exclusions for other illness * Other active malignancy or history of secondary malignancy. * Refractory nausea and vomiting, malabsorption, external biliary shunt * Infection: Patients who have a known active infection (excluding documented fungal infection of the nail beds) within 28 days prior to enrollment that has not completely resolved. * Major surgical procedure or significant traumatic injury within 28 days prior to enrollment, or anticipation of need for major surgical procedure during the course of the study. Placement of a vascular access device or minor surgery is permitted within fourteen (14) days prior to study enrollment (provided that the wound has healed). * History of significant bowel resection that would preclude adequate absorption or other significant malabsorptive disease. * History of pneumonitis. * Ophthalmologic considerations: Patients with known significant ophthalmologic conditions or known risk factors for retinal vein occlusion are not eligible. Specifically, patients with a history of retinal vein occlusion (RVO), retinal detachment, retinal pathology on ophthalmologic exam, retinopathy of prematurity, central serous chorioretinopathy (CSSCR), neovascular retinopathy, intraocular pressure \> 21 mmHg, and predisposing factors to RVO (e.g., uncontrolled hypertension, diabetes, or hyperlipidemia, coagulopathy) will be excluded. Patients with longstanding and stable ophthalmologic findings secondary to existing conditions are eligible with appropriate written documentation and approval from Study Chair. * History of solid organ transplantation: Patients who have received a prior solid organ transplantation are not eligible. * Any other disease, metabolic or psychological dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that in the opinion of the investigator contraindicates use of an investigational drug or places the patient at unacceptable risk from treatment complications. * History of clinically significant cardiac dysfunction, including the following: * Clinically significant cardiac arrhythmias including brady-arrhythmias and/or patients who require anti-arrhythmic therapy (with the exception of beta blockers or digoxin). Patients with controlled atrial fibrillation are not excluded. * Unstable arrhythmia * Unstable angina, or new-onset angina within 3 months prior to initiation of study treatment * Symptomatic congestive heart failure, defined as New York Heart Association Class II or higher * Myocardial infarction within 3 months prior to initiation of study treatment * Known chronic human immunodeficiency virus (HIV). * History of Grade ≥ 2 CNS hemorrhage or history of any CNS hemorrhage within 28 days of enrollment. * Female patients who are pregnant or lactating. Pregnant or lactating women will not be entered on this study because there is no available information regarding human fetal or teratogenic toxicities.