A Study of Botensilimab and Balstilimab for Rectal Adenocarcinoma

Inclusion Criteria: * Willing and able to provide written informed consent for trial. a. If participant is unable to provide written informed consent, the legally authorized representative (LAR) of the person who is being asked to participate in this research study may give consent on the participant's behalf. * Be ≥18 years of age on the date of signing informed consent. * ECOG performance status of 0 or 1. * Histologically confirmed rectal adenocarcinoma. * Adenocarcinoma with distal margin of 15 cm or less from the anal verge on endoscopy, staged with endorectal ultrasound (ERUS) or magnetic resonance imaging (MRI) as cT3/cT4 N0 or cT(any) cN1/2. * No evidence of distant metastases * Radiologically measurable or clinically evaluable disease per Protocol Section 13.0. * Tumor specimen that demonstrates intact mismatch repair enzymes by immunohistochemistry or microsatellite stability as demonstrated by NGS or PCR. * Negative pregnancy test done within 14 days prior to beginning treatment, for women of childbearing potential only. Subjects of childbearing potential must be willing to use an adequate method of contraception. Appropriate methods of birth control include abstinence, oral contraceptives, implantable hormonal contraceptives, or double barrier method (diaphragm plus condom). Contraception is required for the course of the study starting with the first dose of study medication through 150 days after the last dose of study medication. Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. * Nonchildbearing potential is defined as follows (by other than medical reasons): 1. ≥45 years of age and has not had menses for \>1 year 2. Patients who have been amenorrhoeic for \<2 years without history of a hysterectomy and oophorectomy must have a follicle stimulating hormone value in the postmenopausal range upon screening evaluation 3. Post-hysterectomy, post-bilateral oophorectomy, or post-tubal ligation. Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound. Tubal ligation must be confirmed with medical records of the actual procedure, otherwise the patient must be willing to use 2 adequate barrier methods throughout the study. * Demonstrate adequate organ function as defined in the Table 6-1 below within 28 days of Cycle 1 Day 1, and all screening labs should be performed within 28 days of treatment initiation. Hematological Absolute neutrophil count (ANC): ≥1,500 /mm\^3 Platelets: ≥100,000 / mcL Hemoglobin: ≥8.0 g/dL Renal Serum creatinine OR measured or calculated creatinine clearance (GFR can also be used in place of creatinine or CrCl): ≤1.5 × upper limit of normal (ULN) OR ≥60 mL/min for subject with creatinine levels \> 1.5 × institutional ULN AST (SGOT) and ALT (SGPT): ≤ 2.5 × ULN Coagulation International normalized ratio (INR) or Prothrombin time (PT) or activated partial thromboplastin time (aPTT): For patients not taking warfarin: INR ≤ 1.5 or PT ≤ 1.5 x ULN; and either PTT or aPTT ≤ 1.5 x ULN. Patients on warfarin may be included on a stable dose with a therapeutic INR \<3.5 Exclusion Criteria: * Recurrent rectal cancer. * Prior pelvic radiation therapy, chemotherapy, or surgery for rectal cancer. * Tumor is causing symptomatic bowel obstruction (patients who have a temporary diverting ostomy are eligible). * Other invasive malignancy ≤ 2 years prior to registration. Exceptions are non-melanoma skin cancer that has undergone potentially curative therapy and in situ cervical carcinoma. * Active infection requiring systemic therapy. * Other anticancer or experimental therapy. No other experimental therapies (including chemotherapy, radiation, hormonal treatment, antibody therapy, immunotherapy, gene therapy, vaccine therapy, angiogenesis inhibitors, matrix metalloprotease inhibitors, thalidomide, anti-VEGF/Flk-1 monoclonal antibody or other experimental drugs) of any kind are permitted while the patient is receiving study treatment. * Known history of interstitial lung diseases/pneumonitis * Known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Known active hepatitis B (e.g., HbsAg reactive) or hepatitis C (e.g., HCV RNA \[qualitative\] is detected). * Live vaccination within 28 days prior to receiving the first dose of immunotherapy. The use of inactivated seasonal influenza vaccines (e.g., Fluzone®) will be permitted on study without restriction. * Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccine or booster \< 7 days before C1D1. For vaccines requiring more than 1 dose, the full series should be completed prior to C1D1, when feasible. Booster shot not required but also must be administered \> 7 days from C1D1 or \> 7 days from future cycle on study * Clinically significant (i.e., active) cardiovascular disease: cerebral vascular accident/stroke or myocardial infarction within 180 days of enrollment, unstable angina, congestive heart failure (New York Heart Association class ≥ III), or serious uncontrolled cardiac arrhythmia requiring medication. a. QTcF (QT interval corrected using Fridericia's formula) of ≥450 ms. * Known active tuberculosis. * Receiving systemic corticosteroid therapy 1 week prior to the first dose of study drug or receiving any other form of systemic immunosuppressive medication. a. Corticosteroid use as a premedication for IV contrast allergies/reactions is allowed. Subjects who are receiving daily corticosteroid replacement therapy are also an exception to this rule. Daily prednisone at doses of ≤ 7.5 mg or equivalent hydrocortisone dose are examples of permitted replacement therapy. Use of inhaled or topical corticosteroids is permitted. * Has ongoing or recent (within 5 years) evidence of significant autoimmune disease or any other condition that required treatment with systemic immunosuppressive treatments. The following are not exclusionary: vitiligo, childhood asthma that has resolved, endocrinopathies (such as hypothyroidism or type 1 diabetes) that require only hormone replacement. * Prior allogeneic tissue/solid organ transplant, except for corneal transplants.