Although peer support interventions benefit patients throughout the cancer care continuum, most existing interventions have been developed and tested in patients with solid tumors. Patients with hematologic malignancies undergoing hematopoietic stem cell transplantation (HSCT) can especially benefit from structured peer support interventions to potentially address persistent gaps in psychosocial care. In the absence of evidence-based structured peer support interventions for HSCT recipients, the study investigators developed the STEPP intervention. STEPP pairs patients with HSCT survivors who are trained by clinical psychologists to deliver five manualized phone sessions prior to transplantation and through acute recovery. With this multi-site randomized clinical trial, the investigators aim to find out whether STEPP can improve psychological distress and quality of life, compared to a minimally enhanced usual care control condition, using validated assessment tools.