This study is being done to answer the main question of: Do patients with colorectal cancer that cannot be removed by surgery, that is treated with two new immunotherapy drugs, botensilimab and balstilimab, live longer? Other important questions include: Is their quality of life better? Do their tumours slow in growth or possibly shrink in size? Are there markers in their tumour or blood that can predict whether they achieve any of these benefits? In addition, the study is done to confirm the safety of these immunotherapy drugs and to determine how long it takes for the body to metabolize them.

This study is being done to find out if this approach (taking botensilimab and balstilimab) is better or worse than the usual approach for colorectal adenocarcinoma that cannot be removed by surgery. The usual approach is defined as care most people get for colorectal adenocarcinoma that cannot be removed by surgery and that has become resistant to treatment with available therapies.

The usual approach for patients who are not in a study is supportive care with drugs and other treatments that may help to make them feel better or may improve their quality of life. This treatment is known as "best supportive care." Although patients with best supportive care can feel better for some months, the cancer usually continues to grow.

Inclusion Criteria:

• Must have histologically confirmed colorectal adenocarcinoma that is not deficient mismatch repair (dMMR) or microsatellite instability-high (MSI-H).
• Received and failed all prior available therapies, such that the standard of care for the patient would be best supportive care (BSC).
• Must have an Eastern Cooperative Oncology Group (ECOG) performance status 0, or 1.
• Must have presence of measurable or evaluable disease as defined by Response Evaluation Criteria in Solid Tumours (RECIST 1.1).
• A life expectancy of ≥ 12 weeks at the time of study entry.
• Must be ≥ 18 years of age.
• Participants must consent to provision of, and investigator must agree to submit, a representative archival formalin fixed paraffin block of tumour tissue for correlative analyses when tumour tissue is available.
• Participants must have adequate organ and marrow function measured within 14 days prior to randomization.
• Participant is able (i.e. sufficiently fluent) and willing to complete the quality of life and health utility questionnaires in either English or French.
• Participant consent must be appropriately obtained in accordance with applicable local and national regulatory requirements.
• Participants must be accessible for treatment and follow-up. Investigators must assure themselves the participants enrolled on this trial will be available for complete documentation of the treatment, adverse events, and follow-up.
• In accordance with CCTG policy, protocol treatment is to begin within 2 working days of participant enrolment.
• Participants of childbearing potential or partners of participants of childbearing potential must have agreed to use a highly effective contraceptive method

Exclusion Criteria:

• Participants 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 may be eligible for this trial, however, consultation with CCTG in advance of enrolment is required.
• A history of primary immunodeficiency, solid organ transplant or allogeneic bone marrow transplant.
• Current or prior use of immunosuppressive medication within 7 days before the first dose of study drugs, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed 10 mg/day of prednisone, or an equivalent corticosteroid.
• Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease that has required systemic treatment within 2 years of the start of study drug.
• Active or uncontrolled intercurrent illness.
• Active brain metastases or leptomeningeal metastases.
• Receipt of live attenuated vaccination administered within 30 days prior to randomization.
• Lactating women who choose to breast feed.
• Any active disease condition which would render the protocol treatment dangerous or impair the ability of the participant to receive protocol therapy.
• Any condition that does not permit compliance with the protocol.
• Receipt of anti-cancer chemotherapy or biologic therapy within the lesser of i) 21 days, or ii) the usual cycle length of the regimen prior to the first planned dose of study drug.
• Receipt of radiotherapy or investigational agents within four weeks of first planned dose of study drug.
• Any unresolved toxicity (≥ CTCAE grade 2) from previous anti-cancer therapy.
• Known allergy or hypersensitivity to any of the study drugs or any of the study drug excipients.
• History of partial or complete bowel obstruction within the last 3 months prior to study enrolment, signs/symptoms of bowel obstruction or known radiologic evidence of impending obstruction.
• Refractory ascites defined as requiring 2 or more therapeutic paracenteses within the last 4 weeks or ≥ 4 times within the last 3 months or ≥ 1 time within the last 2 weeks or requiring diuretics within 2 weeks prior to study enrolment.
• Active or ongoing diarrhea of CTCAE grade 2 or higher.
• Tumour is mismatch repair deficient (dMMR) or microsatellite instability- high (MSI-H) per a standard local testing method.
• Prior exposure to anti-PD-1/PD-L1/CTLA-4 therapy.