This study is being done to evaluate if by adding a 3rd drug (irinotecan) to the standard regimen of FOLFOX or CAPOX given following long-course chemoradiation for patients with locally advanced rectal cancer can increase the clinical complete response rate (tumor disappears by exam, endoscopy, and imaging).

The usual approach for patients who are not in a study is treatment with chemoradiation followed by radical surgery then possibly chemotherapy after surgery, or a combination of chemotherapy then chemoradiation then radical surgery.

FOLFOX (Leucovorin, 5-Fluorouracil, Oxaliplatin), CAPOX (Capecitabine, Oxaliplatin), and FOLFIRINOX (Leucovorin, 5-Fluorouracil, Irinotecan, Oxaliplatin) are all approved by the U.S. Food and Drug Administration (FDA) for rectal cancer. However, FOLFIRINOX is typically not used until FOLFOX stops working.
   
All participants in this study will get long-course chemoradiation (the usual treatment) for up to 5 weeks. After that, participants will be randomized into one of two groups. Randomization is like flipping a coin and there is a 50/50 chance of being assigned to either group.

• In Group 1, participants will receive the usual drugs (FOLFOX or CAPOX) after long-course chemoradiation. Those receiving FOLFOX (Leucovorin, 5-Fluorouracil, Oxaliplatin) will get these drugs through a vein in the arm on day 1 of each cycle for 8 cycles. Each cycle lasts 14 days. Those receiving CAPOX (Capecitabine, Oxaliplatin) will get oxaliplatin through a vein in the arm on day 1 of each cycle and will take capecitabine by mouth on days 1-14 of each cycle for 5 cycles. Each cycle lasts 21 days.
• In Group 2, participants will receive FOLFIRINOX (Leucovorin, 5-Fluorouracil, Irinotecan, Oxaliplatin) after long-course chemoradiation. Participants will get these drugs through a vein in the arm on day 1 of each cycle. Each cycle lasts 14 days and there are 8 total cycles.

After participants finish treatment, they will be checked about every 4 months for 2 years after treatment. After that, they will be checked about every 6 months for 3 years. Total study participation will last approximately 5 years after treatment.