Capecitabine/Oxaliplatin Chemotherapy and Cemiplimab With or Without Fianlimab or REGN7075 in Locally Advanced Rectal Cancer

Inclusion Criteria: * Age ≥18 years. * Eastern Cooperative Oncology Group (ECOG) performance status 0 - 1. * Rectal cancer (with tumor tissue present at or below the peritoneal reflection) as determined by MRI pelvis or endoscopic ultrasound. * Have histologically proven mismatch repair proficient (pMMR) or microsatellite stable (MSS) rectal adenocarcinoma. * Must not have received any prior systemic treatment or radiation. * Candidate for sphincter-sparing surgical resection after neoadjuvant therapy according to the primary surgeon. * Patients have the following clinical staging: * cT2 node-positive: * T: Tumor is invading the muscularis propria but has not grown through it to the serosa * N: At least 1 perirectal lymph node ≥5 mm and no more than 4 perirectal lymph nodes \>10 mm in short axis * M: No evidence of metastasis * cT3 node-negative * T: Tumor has grown through the muscularis propria into the serosa but has not invaded nearby organs * N: No perirectal lymph nodes ≥ 5 mm in size that suggest tumor involvement * M: No evidence of metastasis * cT3 node-positive * T: Tumor has grown through the muscularis propria into the serosa but has not invaded nearby organs * N: At least 1 perirectal lymph node ≥ 5 mm and no more than 4 perirectal lymph nodes \> 10 mm in size in short axis * M: No evidence of metastasis * Absence of distant metastases on CT or MRI imaging * Patients must have adequate organ and marrow function defined by study-specified laboratory tests and procedures. * LVEF assessment with documented LVEF ≥ 50% by either TTE or MUGA (TTE preferred) within 6 months from first study drug administration. * For both Women and Men, must use acceptable form of birth control while on study. * Ability to understand and willingness to sign a written informed consent document. Exclusion Criteria: * Have received an investigational agent or used an investigational device within 28 days of the first dose of study drug. * Have expected to require any other form of systemic or localized antineoplastic therapy while on study. * Have had surgery within 28 days of dosing of investigational agent, excluding minor procedures (dental work, skin biopsy, etc.). * History of prior treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA4, or anti-Lag-3 antibodies for any reason. * Currently using any chronic systemic steroids. * History of severe hypersensitivity reaction to any monoclonal antibody. * History of encephalitis, meningitis, dementia, Parkinson's or uncontrolled seizures within 1 year prior to the first dose of study drug. * Uncontrolled infection of HIV, HBV, HCV, or Tuberculosis. * Uncontrolled intercurrent illness including, but not limited to, uncontrolled infection, symptomatic congestive heart failure, unstable angina, cardiac arrhythmia, metastatic cancer, or psychiatric illness/social situations that would limit compliance with study requirements. * Active autoimmune disease. * Any tissue or organ allograft, regardless of need for immunosuppression, including corneal allograft. * Patient has a pulse oximetry of \<92% on room air. * Patient is on supplemental home oxygen. * Has clinically significant heart disease. * Troponin T (TnT) or troponin I (TnI) \> 2x institutional ULN at baseline. * Conditions, including alcohol or drug dependence, intercurrent illness, or lack of sufficient peripheral venous access, that would affect the patient's ability to comply with study visits and procedures. * Patient is pregnant or breastfeeding. * Unwilling or unable to follow the study schedule for any reason. * Patient received a live vaccine within 30 days of planned start of study medication. * Receipt of COVID-19 vaccination within 1 week of planned start of study medication or for which the planned COVID-19 vaccinations would not be completed 1 week prior to start of study medication. * Patients with T4 disease or N2 disease (as defined by \>/= 4 lymph nodes, each greater or equal to 10 mm in short axis). * Evidence that the tumor is adjacent to (defined as within 3 mm of) the mesorectal fascia on pre-operative MRI or endorectal ultrasound or pelvic CT scan. * Patients with symptomatic untreated bowel obstruction due to rectal cancer.