The standard or usual treatment for this disease is treatment with drugs and other treatments that may help to make a patient better or may improve their quality of life. This treatment is known as "best supportive care" (BSC). Although patients with best supportive care can feel better for some months, the cancer usually continues to grow.

Durvalumab is a new type of drug for many types of cancer. Laboratory tests show that it works by allowing the immune system to detect cancer and reactivate the immune response. This may help to slow down the growth of cancer or may cause cancer cells to die. Durvalumab has been shown to shrink tumours in animals and has been studied in a few people and seems promising but it is not clear if it can offer better results than standard treatment alone.

Tremelimumab is a new type of drug for various types of cancers. It works in a similar way to durvalumab and may improve the effect of durvalumab. This may also help slow the growth of the cancer cells or may cause cancer cells to die. Tremelimumab has been shown to shrink tumours in animals and has been studied in a few people and seems promising but it is not clear if it can offer better results than standard treatment alone when used with durvalumab.

Combinations of durvalumab and tremelimumab have also been studied and when combined have been shown to increase tumour shrinkage in animals compared to either drug alone and while the combination has been studied in a few people, it is not clear if it can offer better results than standard treatment.

Inclusion Criteria:

• Must have histologically or pathologically confirmed advanced (metastatic or locally advanced) colorectal cancer that is unresectable.
• Received a prior thymidylate synthase inhibitor (e.g. 5-fluorouracil (5-FU), capecitabine, raltitrexed, UFT) for metastatic disease or as adjuvant therapy. A thymidylate synthase inhibitor may have been given in combination with oxaliplatin or irinotecan.
• Received and failed an irinotecan -containing regimen (i.e. single-agent or in combination) for treatment of metastatic disease, OR relapsed within 6 months of completion of an irinotecan-containing adjuvant therapy, OR have documented unsuitability for an irinotecan-containing regimen.
• Received and failed an oxaliplatin-containing regimen (i.e. single-agent or in combination) for treatment of metastatic disease, OR relapsed within 6 months of completion of an oxaliplatin-containing adjuvant therapy OR have documented unsuitability for an oxaliplatin-containing regimen.
• For patients with colorectal cancer that is RAS-wild type:

Received and failed a cetuximab or panitumumab-containing regimen (i.e. single-agent or in combination) for treatment of metastatic disease OR have documented unsuitability for a cetuximab or panitumumab-containing regimen

• Patient prior treatment with VEGF targeting therapy, such as bevacizumab, aflibercept, ramucirumab, or regorafenib, is permitted but not mandatory. Reasons not used are to be documented.
• Patient prior treatment with TAS-102 (an agent composed of a combination of trifluorothymidine (FTD) and tipiracil hydrochloride (TPI)), is permitted but not mandatory.
• The only remaining standard available therapy as recommended by the Investigator, in consultation with the patient, is best supportive care.
• Must have presence of measurable or evaluable disease as defined by Response Evaluation Criteria in Solid Tumours (RECIST 1.1).
• Imaging investigations including CT/MRI of chest/abdomen/pelvis or other scans as necessary to document all sites of disease done within 28 days prior to randomization.
• Must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
• Life expectancy of ≥ 12 weeks at the time of study entry.
• Must be ≥ 18 years of age.
• Women/men of childbearing potential must have agreed to use a highly effective contraceptive method.
• Patient must consent to provision of, and investigator(s) must confirm adequacy of tissue, and confirm access to and agree to submit within 4 weeks of randomization to the CCTG Central Tumour Bank, a representative formalin fixed paraffin block of tumour tissue in order that the specific correlative marker assays may be conducted.
• Patient must consent to provision of samples of blood in order that the specific correlative marker assays
• Patient is able (i.e. sufficiently fluent) and willing to complete the quality of life questionnaires in either English or French.

Patients must be accessible for treatment and follow-up. Investigators must assure themselves the patients randomized 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 patient randomization.
• The patient is not receiving therapy in a concurrent clinical study and the patient agrees not to participate in other clinical studies during their participation in this trial while on study treatment.