Selumetinib and Cetuximab in Treating Patients With Refractory Solid Tumors

Inclusion Criteria: * In the dose escalation cohorts: Patients must have histologically confirmed malignancy that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective; histology can be based on either the primary tumor or metastases * In the MTD expansion cohort: Patients must have biopsy proven K-RAS mutant, metastatic colorectal cancer that has progressed on at least 2 prior standard therapies; K-RAS mutation status must be verified by a CLIA-certified laboratory (NOTE: colorectal patients enrolled during the dose escalation portion do not need to be K-RAS mutant in order to be eligible) * Patients must be at least 4 weeks since prior chemotherapy, 6 weeks if the last regimen included nitrosureas or mitomycin C; prior radiation is allowed as long as the radiation was completed 4 weeks prior to study treatment and no more than 35% of marrow irradiated * ECOG performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy of greater than 3 months * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin within normal institutional limits * AST(SGOT)/ALT(SGPT) =\< 2.5 X institutional upper limit of normal (AST and ALT =\< 5.0 X institutional upper limit of normal will be permitted if liver metastases are present) * Creatinine =\< 1.5 X institution upper limit of normal OR creatinine clearance \>= 45 mL/min/1.73 m\^2, as calculated by Cockroft-Gault formula, for patients with creatinine levels above institutional normal * Patients may have received prior cetuximab * The effects of AZD6244 on the developing human fetus are unknown; for this reason and because small molecule kinase inhibitors as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception prior to study entry and for 16 weeks following the last dose of study treatment. Acceptable methods of birth control include implants, injectables, combined oral contraceptives, (which must all be combined with barrier methods of contraception), some IUDs, sexual abstinence, and vasectomized partner; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document * Patients with brain metastases that have been treated and stable for 2 months will be eligible for this study * Subjects undergoing anti-coagulation therapy with LMWH and warfarin are eligible; subjects receiving both warfarin and AZD6244 should have more frequent PT/INR monitoring Exclusion Criteria: * Patients who have had chemotherapy, radiotherapy or hormonal therapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered (=\< grade 1) from adverse events due to agents administered more than 4 weeks earlier * Concurrent treatment with an investigational agent other than the investigational agent(s) used in this study OR treatment within 4 weeks of study entry with any investigational agent(s) or device(s) * Failure to recover fully (as judged by the investigator) from prior surgical procedures * History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD6244 or other agents used in study * Patients taking high doses (more than recommended daily dose) of vitamin E will be excluded; patients can discontinue use of high dose vitamin E prior to study entry to be considered eligible * Any condition (e.g., gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for IV alimentation, prior surgical procedures affecting absorption, or active peptic ulcer disease) that impairs their ability to swallow and retain AZD6244 capsules * Patients with malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel are excluded; subjects with ulcerative colitis, inflammatory bowel disease, or a partial or complete small bowel obstruction are also excluded * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, prior cardiomyopathy, LVEF \< 50%, unstable angina pectoris, cardiac arrhythmia (i.e. atrial fibrillation), or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because AZD6244 is a small molecule kinase inhibitor with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with AZD6244, breastfeeding should be discontinued if the mother is treated with AZD6244; these potential risks may also apply to other agents used in this study * HIV-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with AZD6244; in addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated * Patients who are serologically positive for Hepatitis B or C, or have a history of liver disease, other forms of hepatitis or cirrhosis are ineligible * Use of strong CYP1A2 or 3A4 inducers and/or inhibitors (for example, but not limited to, ketoconazole, rifampicin, atazanavir, clarithromycin, indinavir, itraconazole, nefazodone, nelfinavir, ritonavir, saquinavir, telithromycin, troleandomycin (TAO), voriconazole, grapefruit or grapefruit juice, rifabutin, rifapentine, phenytoin, carbamazepine, phenobarbital and St. John's Wort) is not permitted while on study or within 7 days prior to study enrollment