Study of Durvalumab (MEDI4736) (Anti-PD-L1) and Trametinib (MEKi) in MSS Metastatic Colon Cancer

Study Drug Administration: Each cycle is 28 days. Participant will take trametinib tablets by mouth every day with at least 8 ounces of water. Each dose should be taken at about the same time each day, 1 hour before or 2 hours after a meal. Participant should not crush, cut, or chew the tablets. If participant misses a dose of trametinib, participant may take the tablets as soon as participant remembers but only if participant's next scheduled dose is at least 12 hours later. If participant's next scheduled dose is less than 12 hours, participant should wait and take participant's next dose as scheduled. Participant will take trametinib alone for the first 7 days of the study and then participant will begin receiving it in combination with durvalumab. Every 4 weeks, participant will receive durvalumab by vein over about 60 minutes. Length of Treatment: Participant will be able to receive the study drugs for as long as the doctor thinks it is in participant's best interest. Participant no longer will take the study drugs if intolerable side effects occur or if the study doctor decides that the drugs are no longer working. It is expected that participation in this study may last about 12 months. Participation in this study will be over after follow-up. Study Visits: On Day 1 of Weeks 0, 2, 4, 6, 12, and then every 4 weeks after that (Weeks 16, 20, 24, and so on): * Participant will have a physical exam. * Blood (about 6 tablespoons) will be drawn for routine tests, immune system testing, and biomarker testing. * If participant had a biopsy at screening, participant will have another biopsy during Week 4 to check the status of the disease and for biomarker testing. Depending on when participant joins the study, this biopsy may be optional. On Day 1 of Week 8: * Participant will have a physical exam. * Blood (about 6 tablespoons) will be drawn for routine tests, immune system testing, and biomarker testing. * Participant will have a CT scan. On Day 1 of Week 16 and then every 8 weeks after that (Weeks 24, 32, 40, and so on), participant will have a CT scan. End-of-Treatment: About 28 days after participant's last dose of study drugs, participant will have a physical exam. Follow-Up: After participant's end-of-treatment visit, participant will be called by the study staff every 3 months for up to 18 months to ask how participant is doing. Each call should last about 5-10 minutes.