This phase II trial studies circulating cell-free tumor DNA testing to guide treatment with regorafenib or TAS-102 in patients with colorectal cancer that has spread to other areas of the body. Studying samples of blood from patients with colorectal cancer may help doctors understand how well patients respond to treatment. Regorafenib and TAS-102 may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. It is not yet known how well ctDNA testing works in guiding treatment with regorafenib and TAS-102 for patients with advanced or metastatic colorectal cancer.

PRIMARY OBJECTIVES:

I. To evaluate the ability of early change in circulating tumor-derived deoxyribonucleic acid (ctDNA) (ctDNA-early dynamic changes [EDC] or A ctDNA) during systemic therapy in metastatic colorectal cancer (mCRC) to predict radiographic progression (only standard of care [SOC] arm).

II. To evaluate differences in clinically significant treatment-related adverse events (TRAEs) of interest (grade 3/4 toxicity per National Cancer Institute (NCI)-Common Terminology Criteria for Adverse Events (CTCAE) version 4.0, intolerable grade 2 toxicity or any toxicity requiring dose reduction) between SOC and ctDNA arm.

SECONDARY OBJECTIVES:

I. To evaluate differences in patient-reported outcomes (PROs) between SOC and ctDNA arm.

II. To compare Response Evaluation Criteria in Solid Tumors (RECIST) duration of complete response (DCR) (partial response [PR] and stable disease [SD]) between SOC and ctDNA arm.

III. To evaluate differences in overall survival (OS) between SOC and ctDNA arm.

IV. To evaluate differences between SOC and ctDNA arm with regards to emergency severity indices (ESIs): Hospitalizations/emergency room visits.

V. To evaluate differences between SOC and ctDNA arm with regards to ESIs: Need for medical interventions (blood transfusions and intravenous [IV] hydration).

VI. To evaluate cost-effectiveness associated with both strategies, i.e. SOC strategy and ctDNA strategy in treatment of mCRC.

VII. To compare time to deterioration of Eastern Cooperative Oncology Group (ECOG) performance status (PS) between SOC and ctDNA arms.

VIII. To compare time to deterioration of PROs between SOC and ctDNA arms. IX. To evaluate differences in proportion of patients referred to clinical trial after completion of therapy between SOC and ctDNA arms.

OUTLINE: Patients are randomized to 1 of 2 arms.

ARM I: Patients undergo ctDNA testing and depending on the results receive either regorafenib orally (PO) on days 1-21, trifluridine and tipiracil hydrochloride (TAS-102) PO twice daily (BID) on days 1-5 and 8-12, or regorafenib PO on days 1-21 and TAS-102 PO BID on days 1-5 and 8-12. Treatment repeats every 28 days in the absence of disease progression or unacceptable toxicity.

ARM II: Patients receive regorafenib or TAS-102 per standard of care. Treatment continues in the event of disease stability or regression as per discretion of treating physician or absence of disease progression.

After completion of study treatment, patients are followed up at 2 weeks and then monthly for up to 18 months.

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.