Additional Study Information: Many people who receive antidepressant treatment for their depression do not get an adequate response to the medicines they are taking. If someone has tried two or more antidepressants and they have failed, this is sometimes referred to as treatment-resistant depression or TRD. The COMP006 study is looking into a new treatment approach for people with TRD using an investigational medicine (psilocybin) given with psychological support. The study is suitable for people who have been diagnosed with major depression and are currently experiencing a recurrent or single episode of depression but that have not responded to antidepressant treatment. COMP006 is a three-part study which will last up to 62 weeks. Reimbursement for reasonable, out-of-pocket expenses for travel and other expenses may be available to qualified individuals. The primary aim of the study is to assess the effectiveness and safety of different doses of the investigational medication for reducing symptom severity in TRD, when administered with psychological support. This will be assessed in a 9-week, blinded part of the study (Part A), during which neither participant nor study doctors will know which dose each person has received. The length of time that the investigational medication may affect symptoms and long-term safety of the study drug, and the effectiveness and safety of re-treatment will be assessed in a 17-week single-dose, double-blind re-treatment part (Part B). A 26-week open-label treatment part (Part C) will be offered to participants who are eligible based on their outcome in Parts A and B. Throughout Parts A, B, and C, study visits will include physical examination, vital signs, electrocardiograms, blood collection, urine collection, and psychological assessments. As TRD is a chronic condition in which relapse is common, the incorporation of these additional parts in a single study allows for important long-term monitoring and participant support.