A Phase II Novel Exploratory Study to Test Neoadjuvant Immunotherapy Combinations in Patients With Resectable Colon Cancer (NEST3)

Inclusion Criteria: * Documented informed consent of the participant and Legally Authorized Representative (when applicable) * Assent, when appropriate, will be obtained and documented for adults lacking capacity per institutional guidelines * Agreement to allow the use of tissue from past and future surgery and standard of care biopsies * Age: ≥ 18 years * Eastern Cooperative Oncology Group (ECOG) ≤ 2 * Histologically confirmed or cytologically confirmed colorectal adenocarcinoma. Patients with high grade dysplasia on histology plus unequivocal endoscopic or radiological evidence of invasive cancer are eligible. Patients diagnosed with rectal cancer who will be treated like colon cancer with curative-intent surgery first and no radiation are also eligible, including: * Upper rectum or rectosigmoid considered as non-rectal and not undergoing neoadjuvant treatment * The tumor component should not extend to less 12 cm from the anal verge. * Any patient with rectal cancer for whom radiotherapy is not advised is included in this protocol (i.e., excluding rectal adenocarcinomas warranting treatment with chemoradiation) * Microsatellite stability by mismatch repair by immunohistochemistry, polymerase chain reaction and/or other Clinical Laboratory Improvement Amendments (CLIA) certified next generation sequencing. Only patients with mismatch repair proficient or microsatellite stable (pMMR/MSS) tumors are allowed to enroll in the study * Candidate for and planning a curative resection. Must have surgeon identified * T4, N+ (American Joint Committee on Cancer \[AJCC\] TNM staging criteria), or both by central radiographic assessment. * Note: Patients with T3N0 stage IIA are excluded. Stage IIB, IIC, IIIA, IIIB, and IIIC are included. Patients with stage IV disease are excluded * Absolute neutrophil count (ANC) ≥ 1,500/mm\^3 * Platelets ≥ 75,000/mm\^3 * NOTE: Platelet transfusions are not permitted within 14 days of platelet assessment * Hemoglobin ≥ 8 g/dL * NOTE: Red blood cell transfusions are permitted. Patients should not have active clinically significant bleeding requiring regular transfusions. Iron infusions are also allowed * Total bilirubin ≤ 1.5 X upper limit of normal (ULN) (unless has Gilbert's disease, in which case the liver function tests must meet the other eligibility in the protocol) * Aspartate aminotransferase (AST) ≤ 3.0 x ULN * Alanine aminotransferase (ALT) ≤ 3.0 x ULN * Creatinine clearance of ≥ 40 mL/min per 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). * The following are acceptable birth control methods for this study: Surgical sterilization (tubal ligation or hysterectomy for women, or vasectomy for men), double-barrier methods (i.e. condoms, diaphragm, cervical cap, or sponge, used together with spermicidal gel or foam), intrauterine device (IUD) (i.e. Progestin, Copper), or hormonal contraceptives (birth control patches, implants, pills, rings, or injections) Exclusion Criteria: * Any treatment for colorectal cancer prior to enrollment that includes (but not limited to) chemotherapy, surgery, radiation, immunotherapy and/or biological therapy. * Note: Surgical intervention e.g. a diverting ostomy to relieve an obstruction from colorectal cancer, those patients will be allowed to enter the study as long as no distant metastatic disease * 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 * Herbal medications that require a prescription or are anti-cancer * Other active malignancy. Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. Please note: patients with more than 1 colorectal cancer tumor at diagnosis (as long as no stage IV disease) are allowed to participate. Pathologic response to each of the tumors will be examined * Active acute colonic obstruction. Patients whose obstruction is relieved by a successful defunctioning stoma are allowed once recovered to a fitness level consistent with the other eligibility criteria * 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 or current evidence of any condition, co-morbidity, therapy, 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 * Uncontrolled infection with human Immunodeficiency virus (HIV). Patients on stable highly active antiretroviral therapy (HAART) are eligible. Serological testing for HIV at screening is not required * Uncontrolled infection with hepatitis B virus. Patients who are receiving or who have received anti-HBV therapy 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. Serological testing for HCV at screening is not required * 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)