The current standard of care in most uses of psychedelic medicines for the treatment of psychiatric indications includes the provision of a supportive therapeutic context before, during, and after drug administration. A diversity of psychedelic-assisted psychotherapy (PAP) models has been created to meet this need. The current article briefly reviews the strengths and limitations of these models, which are divided into basic support models and EBT-inclusive therapy models. It then discusses several shortcomings both types of models share, including a lack of adequate attention to embodied and relational elements of treatment, and insufficient attention to ethical concerns. The article then introduces the EMBARK model, a transdiagnostic, trans-drug framework for the provision of supportive psychotherapy in PAP clinical trials and the training of study therapists. EMBARK was designed to overcome challenges that prior models have had in conceptualizing therapeutic change in psychedelic treatment, incorporating elements of non-psychedelic evidence-based therapies, incorporating therapists' prior skills and clinical orientations, delimiting therapist interventions for research standardization, and determining specific factors that contribute to treatment outcomes. The article explains EMBARK's six clinical domains, which represent parallel conceptualizations of how therapists may support therapeutic benefit in PAP treatment, and its four care cornerstones, which reflect therapists' broad ethical responsibility to participants. The article describes how these elements of the model come together to structure and inform therapeutic interventions during preparation, medicine, and integration sessions. Additionally, the article will discuss how EMBARK therapist training is organized and conducted. Finally, it will demonstrate the broad applicability of EMBARK by describing several current and upcoming PAP clinical trials that have adopted it as the therapeutic frame.