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