Testing the Addition of an Anti-Cancer Drug, Irinotecan, to the Standard Chemotherapy Treatment (FOLFOX) After Long-Course Radiation Therapy for Advanced-Stage Rectal Cancers to Improve the Rate of Complete Response and Long-Term Rates of Organ Preservation

This phase II trial compares the effect of irinotecan versus oxaliplatin after long-course chemoradiation in patients with stage II-III rectal cancer. Combination chemotherapy drugs, such as FOLFIRINOX (fluorouracil, irinotecan, leucovorin, and oxaliplatin), FOLFOX (leucovorin, fluorouracil, oxaliplatin, and irinotecan ), and CAPOX (capecitabin and oxaliplatin) 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. FOLFOX or CAPOX are used after chemoradiation as usual treatment for rectal cancer. Giving FOLFIRINOX after chemoradiation may increase the response rate and lead to higher rates of clinical complete response (with a chance of avoiding surgery) compared to FOLFOX or CAPOX after chemoradiation in patients with locally advanced rectal cancer.

PRIMARY OBJECTIVE:

I. To evaluate and compare the clinical complete response (cCR) rates in patients with locally advanced rectal cancer treated with neoadjuvant long-course neoadjuvant radiotherapy (LCRT) followed by neoadjuvant modified fluorouracil, irinotecan, leucovorin, and oxaliplatin (mFOLFIRINOX) versus neoadjuvant LCRT followed by neoadjuvant modified leucovorin , fluorouracil, and oxaliplatin (mFOLFOX6).

SECONDARY OBJECTIVES:

I. To evaluate and compare organ-preservation-time (OPT) between two treatment arms.

II. To evaluate and compare the disease-free survival (DFS) time between the two treatment arms.

III. To evaluate and compare time to distant metastasis between two treatment arms.

IV. To evaluate and compare overall survival (OS) between two treatment arms. V. To evaluate and compare toxicity profiles of total neoadjuvant therapy (TNT) between two treatment arms.

EXPLORATORY OBJECTIVE:

I. Evaluation of circulating tumor deoxyribonucleic acid (ctDNA) kinetics during neoadjuvant therapy \& surveillance and to correlate with radiographic, pathologic, and clinical outcomes.

OUTLINE: Patients are randomized to 1 of 2 arms.

GROUP I: Patients receive long-course chemoradiation therapy on study and then receive either: FOLFOX regimen consisting of leucovorin intravenously (IV), fluorouracil IV, and oxaliplatin IV or CAPOX consisting of capecitabine orally (PO), and oxaliplatin IV on study. Patients undergo computed tomography (CT) scan, magnetic resonance imaging (MRI), and biospecimen collection throughout the trial. Patients also undergo sigmoidoscopy throughout the trial and biopsy during screening.

GROUP II: Patients receive long-course chemoradiation therapy on study and then receive FOLFIRINOX regimen consisting of leucovorin IV, fluorouracil IV, irinotecan IV, and oxaliplatin IV on study. Patients undergo CT scan, MRI scan, and blood specimen collection throughout the trial. Patients undergo sigmoidoscopy throughout the trial and biopsy during screening.

Eligibility Criteria:
Inclusion Criteria:

* Stage: Clinical stage II or III rectal adenocarcinoma defined as T4N0 or any T with node positive disease (any T, N+); also T3N0 requiring abdominal perineal resection (APR) or coloanal anastomosis
* Tumor site: Rectum; =\< 12cm from the anal verge
* No prior systemic chemotherapy, targeted therapy, or immunotherapy; or radiation therapy administered as treatment for colorectal cancer within the past 5 years is allowed
* Not pregnant and not nursing, because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects

  \* Therefore, for women of childbearing potential only, a negative pregnancy test (urine or serum according to institutional guidelines) done =\< 14 days prior to registration is required. Female subjects agree to use highly effective contraception combined with an additional barrier method (e.g, diaphragm, with a spermicide) while on study and for \>= 9 months after last dose of study drug, and the same criteria are applicable to male subjects if they have a partner of childbirth potential. Male subject agrees to use a condom and not donate sperm while in this study and for \>= 6 months after the last treatment
* Age \>= 18 years
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (or Karnofsky \>= 60%)
* Absolute neutrophil count (ANC) \>= 1,500/mm\^3
* Platelet count \>= 100,000/mm
* Creatinine =\< 1.5 x upper limit of normal (ULN) OR calculated (calc.) creatinine clearance \>= 50 mL/min

  \^3
* Total bilirubin =\< 1.5 x upper limit of normal (ULN)
* Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 3 x upper limit of normal (ULN)
* No upper rectal tumors (distal margin of tumor \> 12 cm from the anal verge)
* No recurrent rectal cancer; prior transanal excision, prior distal sigmoid cancer with a low anastomosis
* No known mismatch repair deficient rectal adenocarcinoma
* Human immunodeficiency virus HIV-infected patients on effective anti-retro viral therapy with undetectable viral load within 6 months are eligible for this trial
* Patients with known history or current symptoms of cardiac disease, or history of treatment with cardio toxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification1. To be eligible for this trial, patients should be class 2B or better
* Chronic concomitant treatment with strong inhibitors of CYP3A4 is not allowed on this study. Patients on strong CYP3A4 inhibitors must discontinue the drug for 14 days prior to registration on the study \* Chronic concomitant treatment with strong CYP3A4 inducers is not allowed. Patients must discontinue the drug 14 days prior to the start of study treatment