Additional Study Information: This study is being done to answer the following question: Can we increase the clinical complete response rate (tumor disappears by exam, endoscopy, and imaging) by adding a 3rd drug (irinotecan) to the standard chemotherapy regimens known as FOLFOX or CAPOX, given following long-course chemoradiation for patients with locally advanced rectal cancer? We are doing this study because we want to find out if this approach is better or worse than the usual approach for your rectal cancer. The usual approach is defined as care most people get for locally advanced rectal cancer.