AZD6244 (Selumetinib) in Treating Patients With Multiple Myeloma

Inclusion Criteria: * Confirmed diagnosis of multiple myeloma with relapsed or refractory disease following at least two prior therapies * Measurable disease defined as: * Serum monoclonal protein \>= 1 gm/dL or * Urine monoclonal protein of \>= 200 mg/24 hours, or * Measurable free light chains by free light chain assay of \>= 10 mg/dL with abnormal kappa to lambda free light chain ratio, or * Measurable bone disease, defined as \>= 1 unidimensionally measurable lesion (longest diameter to be recorded) \>= 20 mm with conventional techniques or \>= 10 mm with spiral computed tomography (CT) scan (for patients with lytic bone disease) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Absolute neutrophil count: \>= 1,000/μL (independent of blood cell growth factors) * Platelets: \>= 75,000/μL (independent of blood cell growth factors or transfusion) * Total bilirubin: =\< 1.5 x upper normal limit; however, patients with documented Gilbert's syndrome are eligible * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]): \< 2.5 x upper limit of normal (ULN) * Creatinine: \< 3.0 x ULN * Known human immunodeficiency virus (HIV) infected patients meeting the following characteristics are eligible: * Cluster of differentiation (CD)4 cell count \>= 500/mm\^3 * Meeting either of the following: * Willing to suspend antiretroviral therapy for duration of protocol therapy or * On stable regimen of combination antiretroviral therapy that does not include either zidovudine or stavudine for at least 12 weeks and without evidence of toxicity * No HIV-associated condition that defines acquired immunodeficiency syndrome (AIDS) * Prior allogeneic stem cell transplant is allowed provided that all of the following conditions are met: * \>= 6 months have elapsed since allogeneic transplant * No graft vs. host disease (GVHD) is present * Not currently on immunosuppressive therapy * Women of child-bearing potential must agree to use a medically accepted form of contraception prior to, during, and for four weeks following study treatment; men must agree to use a medically accepted form of contraception prior to, during, and for sixteen weeks following study treatment * Able and willing to provide a written informed consent * Prior palliative and/or localized radiation therapy is permitted, provided at least 14 days have passed from date of last radiation therapy * Pulse oximetry of \>= 95% on room air Exclusion Criteria: * Any concurrent condition or planned treatment that would compromise study objectives or represent an unacceptable patient risk, including but not limited to: * Planned concurrent treatment for multiple myeloma other than bisphosphonates; ongoing corticosteroids for indications other than multiple myeloma allowed as long as the dose does not exceed 60 mg of prednisone per day or equivalent * Persisting effects of any previous or ongoing treatment that might compromise delivery of study treatment or assessment of adverse events * Planned concurrent treatment with any other investigational agents * Cytotoxic chemotherapy less than 2 weeks, or biologic therapy less than 2 weeks, or corticosteroids less than 2 weeks prior to registration * No other malignancy unless the patient has been disease-free for \>= 1 year * Known multiple myeloma of central nervous system or leptomeninges * History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD6244 * Previous mitogen activated protein kinase (MEK) inhibitor use * Uncontrolled hypertension, i.e., persistent blood pressure (BP) of \>= 160/95 * Significant cardiovascular disease (New York Heart Association class II, III or IV cardiac disease), hypertrophic cardiomegaly or restrictive cardiomyopathy, myocardial infarction within the past 6 months, unstable angina, unstable arrhythmia unstable or a need for anti-arrhythmic therapy (use of medication for atrial fibrillation is allowed, if stable for at least 3 months) * Refractory nausea and vomiting, chronic gastrointestinal diseases (e.g. inflammatory bowel disease), or significant bowel resection that would preclude adequate absorption * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant or nursing * Left ventricular ejection fraction (LVEF) =\< 45% by echocardiogram (ECHO) or multigated acquisition scan (MUGA) scan * Any requirement for supplemental oxygen