Inclusion Criteria:

          -  Patients must have histologically or cytologically confirmed colorectal cancer.

          -  Patients must have advanced or metastatic disease with no curative options.

          -  Patients must have radiographically evaluable disease.

          -  Patients must have had at least 2 prior therapies for mCRC (including fluorouracil
             [5-FU], oxaliplatin, irinotecan, bevacizumab; cetuximab/panitumumab [for RAS wild type
             (WT) patients]) and have either progressed on or intolerant to these agents or use of
             these agents is contraindicated.

          -  Patients must be clinically eligible for either regorafenib or TAS-102 as per their
             treating physician.

          -  Patients must have a negative serum pregnancy test done less than are equal to 14 days
             prior to randomization for women of childbearing potential only. Women of child
             bearing potential and men must agree to use adequate contraception (hormonal or
             barrier method of birth control; abstinence) prior to study entry for the duration of
             study participation.

          -  Patients must have ability to complete questionnaire(s) by themselves or with
             assistance.

          -  Patients must have ability to provide informed written consent.

          -  Patients must be willing to return to enrolling institution for follow-up as per study
             schedule.

          -  Patients must be willing to provide blood samples for correlative studies.

          -  Any of the following: Pregnant or nursing women, men or women of childbearing
             potential who are unwilling to employ adequate contraception.

          -  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.

        Exclusion Criteria:

          -  Patient who have received prior TAS-102 are eligible to enroll on the study if they
             can receive regorafenib and vice-versa. Otherwise these patients will be excluded from
             the study.

          -  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 3 months prior to randomization.

          -  Ongoing infection > grade 2 CTCAE version 4.0.

          -  Symptomatic metastatic brain or meningeal tumors unless the patient is > 3 months from
             definitive therapy, has a negative imaging study within 4 weeks of randomization and
             is clinically stable with respect to brain lesions 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]).

          -  Renal failure requiring hematological or peritoneal dialysis.

          -  Patients unable to swallow oral medications.