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 is taking two or more antidepressants and they are failing, this is sometimes referred to as treatment-resistant depression or TRD. We are currently enrolling adult individuals with treatment-resistant depression (TRD) for this research study. The aim of the study is to assess the efficacy and safety of the investigational medication versus placebo for reducing symptom severity in TRD when administered with psychological support. The three-part study, which will last up to 62 weeks, will compare the effectiveness of the active investigational medicine (psilocybin) with a placebo, a substance that has no therapeutic effect. Both the investigational medicine and the placebo will be administered with psychological support. Effectiveness of the investigational medicine compared to placebo will be assessed in a 6-week, single-dose, double-blind, placebo-controlled part of the study (Part A). Durability of efficacy and long-term safety, and the efficacy and safety of re-treatment will be assessed in a 20-week single-dose, double-blind re-treatment part (Part B), and a 26-week open-label treatment part (Part C). Two-thirds of the people in Parts A and B will receive active investigational medicine, and one-third will receive a placebo. If you join the study in Parts A and B neither you nor your study doctors will know which study treatment you are going to receive because the decision is made randomly by a computer and not revealed to anyone. Part C is open-label, so if you are eligible for treatment after completing Parts A and B, you will receive the active investigational product. Throughout Parts A, B, and C, study visits will include physical examination, vital signs, electrocardiograms, blood collection, urine collection, and psychological assessments.