Durvalumab and Tremelimumab and Best Supportive Care vs Best Supportive Care in Patients With Advanced Colorectal Cancer

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.