Phase II Clinical Trial of FOLFOX, Botensilimab, Plus Balstilimab in Patients With Localized Rectal Cancer

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with study principal investigator (PI) approval * Age: ≥ 18 years * Eastern Cooperative Oncology Group (ECOG) ≤ 1 * Histologically confirmed adenocarcinoma of the rectum * Rectal involvement defined as involvement of the rectum within 12 cm proximal from anal verge * Radial margin of at least 3mm from the mesorectal fascia, with no threatened circumferential tumor margin based on MRI. No more than 4 lymph nodes (LN) with short axis \> 1 cm * T3N0, or TxN1 or TxN2 clinical stage based on MRI staging * No evidence of distant metastatic disease based on imaging studies including CT chest and CT or MRI of abdomen and pelvis * Absolute neutrophil count (ANC) ≥ 1,500/mm\^3 * Without bone marrow involvement: Platelets ≥ 100,000/mm\^3 * Hemoglobin ≥ 9g/dL * NOTE: Red blood cell transfusions are not permitted within 14 days of hemoglobin assessment * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) (unless has Gilbert's disease) * Aspartate aminotransferase (AST) ≤ 3.0 x ULN * Alanine aminotransferase (ALT) ≤ 3.0 x ULN * Creatinine \< 1.5 x ULN or clearance of ≥ 40 mL/min per 24 hour urine test or the Cockcroft-Gault formula * Women of childbearing potential (WOCBP): Negative urine or serum pregnancy test * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 9 months for women, and at least 6 months for men, after the last dose of oxaliplatin therapy. If patients discontinue oxaliplatin more than 9 months (females) or 6 months (males) before discontinuation of balstilimab and/or botensilimab, females and males of childbearing potential must use an effective method of birth control or abstain from sexual activity for the course of the study through at least 120 days after the last dose of balstilimab and/or botensilimab * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) Exclusion Criteria: * Any treatment for rectal cancer prior to enrollment that includes (but not limited to) chemotherapy, radiation, and/or biological therapy * Any prior immunotherapy * Patients with a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalent) within 14 days or another immunosuppressive medication within 30 days of the first dose of study treatment. Inhaled or topical steroids, and adrenal replacement steroid doses \> 10 mg daily prednisone equivalent, are permitted in the absence of active autoimmune disease * Prior allogeneic organ transplantation * Surgical intervention within 4 weeks prior to study treatment, except for minor procedures such as port placement or biopsies * Concurrent malignancy other than the diagnosis of rectal cancer, with the exception of curatively resected non-melanoma skin cancer, cervical cancer in situ, prostate cancer Gleason 6 or below that is localized to the prostate, or any other curatively resected cancer from which the patient remains in remission for at least 2 years without treatment * Unstable cardiac disease as defined by one of the following: * Cardiac events such as myocardial infarction (MI) within the past 6 months * NYHA (New York Heart Association) heart failure class III-IV * Uncontrolled atrial fibrillation * Clinically significant uncontrolled illness * Females only: Pregnant or breastfeeding * Prior allergic reaction or hypersensitivity to any of the study drug components * Active autoimmune disease or history of autoimmune disease that required systemic treatment within 2 years before starting treatment, i.e., with use of disease-modifying agents or immunosuppressive drugs (excluding hypothyroidism, vitiligo, and psoriasis that is controlled with topical management) * History of acute thrombotic venous events in the last 30 days before enrollment. If within 30 days, the patient should be on anticoagulants and without symptoms * Any evidence of current interstitial lung disease (ILD) or pneumonitis or a prior history of ILD or non-infectious pneumonitis requiring high-dose glucocorticoids * Psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the study * History or current evidence of any condition, co-morbidity, therapy, any active infections (requiring antibiotics), or laboratory abnormality that might confound the results of the study, interfere with the patient's participation for the full duration of the study, or is not in the best interest of the patient to participate, in the opinion of the treating investigator * Known previous severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection within 10 days for mild or asymptomatic infections or 20 days for severe/critical illness prior to cycle 1 day 1 (C1D1) * Uncontrolled infection with human immunodeficiency virus (HIV). Patients on stable highly active antiretroviral therapy (HAART) with undetectable viral load and normal CD4 counts for at least 6 months prior to study entry are eligible. Serological testing for HIV at screening is not required * Known to be positive for hepatitis B virus (HBV) surface antigen, or any other positive test for HBV indicating acute or chronic infection. Patients who are receiving or who have received anti-HBV therapy and have undetectable HBV deoxyribonucleic acid (DNA) for at least 6 months prior to study entry are eligible. Serological testing for HBV at screening is not required * Known active hepatitis C virus (HCV) as determined by positive serology and confirmed by polymerase chain reaction (PCR). Patients on or who have received antiretroviral therapy are eligible provided they are virus-free by PCR for at least 6 months prior to study entry. Serological testing for HCV at screening is not required * Grade 2 or above neuropathy at the time of enrollment * Dependence on total parenteral nutrition or intravenous hydration * Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)