This phase II trial studies how well TAS-102, irinotecan, and bevacizumab work in treating patients with pre-treated colorectal cancer that has spread to other places in the body (metastatic) or cannot be removed by surgery (unresectable). Drugs used in chemotherapy, such as TAS-102, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Irinotecan may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Immunotherapy with bevacizumab, may induce changes in body's immune system and may interfere with the ability of tumor cells to grow and spread. Giving TAS-102, irinotecan, and bevacizumab may work better in treating patients with colorectal cancer compared to traditional chemotherapy and bevacizumab.

PRIMARY OBJECTIVE:

I. Determine the median progression free survival (PFS) benefit of leucovorin calcium, 5-fluorouracil, and irinotecan (FOLFIRI) naive patients treated with trifluridine and tipiracil hydrochloride (TAS-102) + irinotecan + bevacizumab as compared to historic control groups treated with FOLFIRI + bevacizumab.

SECONDARY OBJECTIVE:

I. Estimate the objective response rate (ORR), median overall survival (OS), and adverse event (AE) profile.

OUTLINE:

Patients receive irinotecan intravenously (IV) over 90 minutes and bevacizumab IV over 30-90 minutes on days 1 and 15. Patients also receive trifluridine and tipiracil hydrochloride orally (PO) twice daily (BID) on days 2-6 and 16-20. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up at 30 days and then every 6 months for up to 2 years.

Inclusion Criteria:

• Advanced colorectal cancer (metastatic or unresectable): Histologically or cytological proven adenocarcinoma of the colon or rectum which is metastatic or otherwise incurable
• Prior treatment with a fluoropyrimidine (5-fluorouracil [5-FU] or capecitabine) and oxaliplatin in the metastatic/unresectable setting OR, recurrence within 12 months of adjuvant therapy with a regimen that included oxaliplatin
• Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1
• Hemoglobin >= 9 g/dL
• Absolute neutrophil count >= 1500/mm^3
• Platelet count >= 100,000/mm^3
• Creatinine < 1.5 upper limit of normal (ULN) or if >= 1.5 x ULN creatinine clearance (CRCL) >= 30 mL/min (by Cockcroft-Gault)
• Bilirubin < 1.5 x ULN
• Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =< 2.5 x ULN or =< 5 x ULN if with hepatic metastases
• Have measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria present
• Participants of child-bearing potential must agree to use adequate contraceptive methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study entry. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately
• Participant must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure

Exclusion Criteria:

• Prior treatment with TAS-102 or irinotecan
• Anti-cancer therapy within 2 weeks of the planned first dose of study medication
• Unresolved toxicities from prior therapy of > grade 1, excluding alopecia or similar toxicities which are not deemed to be clinically significant or put the participant at greater risk. Grade 2 neuropathy is permitted
• Major surgery within 4 weeks of anticipated start of therapy
• Uncontrolled hypertension: systolic blood pressure >= 150, diastolic blood pressure >= 100
• Unstable angina, symptomatic congestive heart failure or cardiac arrhythmia requiring anti-arrhythmic therapy (beta-blockers, calcium channel blockers and digoxin are allowed)
• Arterial or venous thrombotic or embolic events within 3 months of study initiation, unless well controlled on stable anti-coagulation for >= 2 weeks. This excludes uncomplicated catheter associated venous thrombosis
• History of cerebrovascular or myocardial ischemia within 6 months of initiation
• National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version (v) 5.0 grade 3 or greater hemorrhage within the past 4 weeks
• Proteinuria >= 2+, unless 24 hour urine collection demonstrates =< 1 g of protein OR spot protein: creatinine demonstrates a ratio of =< 1
• Untreated brain metastases
• History of abnormal glucuronidation of bilirubin (Gilbert's syndrome)
• History of second primary malignancy within 3 years prior to enrollment, excluding in-situ cervical carcinoma, non-melanoma skin cancer or malignancy of equivalent risk which is highly unlikely to require systemic treatment in the next 2 years
• Have known active infection which would heighten the risk of complications
• Pregnant or nursing female participants
• Unwilling or unable to follow protocol requirements
• Any condition which in the investigator's opinion deems the participant an unsuitable candidate to receive study drug