Lower or Standard Dose Regorafenib in Treating Patients With Refractory Metastatic Colorectal Cancer

Inclusion Criteria: * Histological or cytological documentation of adenocarcinoma of the colon or rectum * Advanced or metastatic colorectal cancer with no curative options available and progression on previous standard therapy, including an EGFR inhibitor if KRAS wild-type * Measurable or non-measurable disease * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0 or 1 * Life expectancy of \>= 3 months * Absolute neutrophil count (ANC) \> 1500/mm\^3 (obtained =\< 7 days prior to randomization) * Platelet count \> 100,000/mm\^3 (obtained =\< 7 days prior to randomization) * Hemoglobin \> 9.0 g/dL (obtained =\< 7 days prior to randomization) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) (obtained =\< 7 days prior to randomization) * Alanine aminotransferase (ALT) and aspartate amino-transferase (AST) =\< 2.5 x ULN (=\< 5 x ULN for subjects with liver involvement of their cancer) (obtained =\< 7 days prior to randomization) * Serum creatinine =\< 1.5 x ULN (obtained =\< 7 days prior to randomization) * International normalized ratio (INR)/partial thromboplastin time (PTT) =\< 1.5 x ULN (obtained =\< 7 days prior to randomization) * NOTE: patients who are therapeutically treated with an agent such as warfarin or heparin will be allowed to participate provided that no prior evidence of underlying abnormality in coagulation parameters exists; close monitoring of at least weekly evaluations will be performed until INR/PTT is stable based on a measurement that is pre-dose as defined by the local standard of care * Alkaline phosphatase limit =\< 2.5 x ULN (=\< 5 x ULN for patients with liver involvement of their cancer) (obtained =\< 7 days prior to randomization) * Negative serum pregnancy test done =\< 7 days prior to randomization, for women of childbearing potential only; note: post-menopausal women (defined as no menses for at least 1 year) and surgically sterilized women are not required to undergo a pregnancy test; the definition of adequate contraception will be based on the judgment of the investigator * Ability to complete questionnaire(s) by themselves or with assistance * Provide informed written consent * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) * Willing to provide blood samples for correlative research and banking purposes Exclusion Criteria: * Prior treatment with regorafenib * Major surgical procedure, open biopsy, or significant traumatic injury =\< 28 days prior to randomization * Congestive heart failure \> New York Heart Association (NYHA) class 2 * Unstable angina (angina symptoms at rest), new-onset angina (begun within the last 3 months) or myocardial infarction less than 6 months prior to randomization * Cardiac arrhythmias requiring anti-arrhythmic therapy; Note: pace makers, beta blockers, or digoxin are permitted * Uncontrolled hypertension; (systolic blood pressure \> 140 mmHg or diastolic pressure \> 90 mmHg despite optimal medical management) * History of or current pheochromocytoma * Arterial or venous thrombotic or embolic events such as cerebrovascular accident (including transient ischemic attacks), deep vein thrombosis or pulmonary embolism =\< 6 months prior to randomization * Ongoing infection \> grade 2 National Cancer Institute (NCI)-Common Terminology Criteria for Adverse Events (CTCAE) version 4.0 * Known history of chronic hepatitis B or C * Patients with seizure disorder requiring medication * Symptomatic metastatic brain or meningeal tumors unless the patient is \> 6 months from definitive therapy, has a negative imaging study within 4 weeks of randomization and is clinically stable with respect to the tumor at the time of randomization; note: patient must not be undergoing acute steroid therapy or taper (chronic steroid therapy is acceptable provided that the dose is stable for one month prior to and following screening radiographic studies) * History of organ allograft (including corneal transplant) * Evidence or history of bleeding diathesis or any hemorrhage or bleeding event \> CTCAE grade 3 =\< 4 weeks prior to randomization * Non-healing wound, ulcer, or bone fracture * Renal failure requiring hematological (hemo-) or peritoneal dialysis * Dehydration CTCAE (version 4.0) grade \>= 1 * Substance abuse, medical, psychological or social conditions that may interfere with the patient?s participation in the study or evaluation of the study results * Known hypersensitivity to any of the study drugs, study drug classes, or excipients in the formulation * Interstitial lung disease with ongoing signs and symptoms at the time of informed consent * Persistent proteinuria of Common Toxicity Criteria (CTC) grade 3 or higher (\>= 3.5 g/24 hours \[hrs\]) * Patients unable to swallow oral medications * Any malabsorption condition * Unresolved toxicity greater than CTCAE (version 4.0) grade 1 attributed to any prior therapy/procedure excluding alopecia and oxaliplatin induced neurotoxicity =\< grade 2 * Albumin levels \< 2.5 g/dl * Any of the following: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * NOTE: men and women of childbearing potential must agree to use adequate contraception beginning at the signing of the informed consent form (ICF) until at least 3 months after the last dose of study drug; the definition of adequate contraception will be based on the judgment of the principal investigator or a designated associate * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Immunocompromised patients and patients known to be human immunodeficiency virus (HIV) positive and currently receiving antiretroviral therapy; NOTE: patients known to be HIV positive, but without clinical evidence of an immunocompromised state, are eligible for this trial * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * Previous or concurrent cancer that is distinct in primary site or histology from colorectal cancer within 3 years prior to randomization EXCEPT for curatively treated cervical cancer in situ, non-melanoma skin cancer and superficial bladder tumors (Ta \[non-invasive tumor\], Tis \[carcinoma in situ\] and T1 \[tumor invades lamina propria\]); note: all cancer treatments for cancers that were distinct in a primary site other than colorectal must be completed at least 3 years prior to randomization (i.e., signature date of the informed consent form) * Pleural effusion or ascites that causes respiratory compromise (\>= CTCAE version 4.0 grade 2 dyspnea) * Concurrent anti-cancer therapy =\< 4 weeks from registration (chemotherapy, radiation therapy, surgery, immunotherapy, biologic therapy, or tumor embolization) * Current use of clobetasol propionate * Use of any herbal remedy (e.g. St. John?s wort \[Hypericum perforatum\]) * Patients unable to ambulate or who have amputations or paralysis of any extremity * History of contact dermatitis to clobetasol propionate or similarly fluorinated steroids or other steroids with the propionate ester