Capecitabine/Oxaliplatin chemo with cemiplimab with or without fianlimab or REGN7075 for 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.