A Platform Protocol to Investigate Post-Transplant Cyclophosphamide-Based Graft-Versus-Host Disease Prophylaxis in Patients With Hematologic Malignancies Undergoing Mismatched Unrelated Donor Peripheral Blood Stem Cell Transplantation

The purpose of this clinical trial is to compare drug combinations to learn which drugs work best to prevent graft-versus-host-disease (GVHD) in people who have received a stem cell transplant. The source of stem cells is from someone who is not related and has a different blood cell type than the study participant. The researchers will compare the new drug combination to a standard drug combination. They will also learn about the safety of each drug combination. Participants will: * Receive the standard or new drug combination after transplant * Visit the doctor's office for check-ups and tests after transplant that are routine for most transplant patients * Take surveys about physical and emotional well-being * Give blood and stool samples.

This platform protocol will evaluate the safety and efficacy of post-transplant cyclophosphamide (PTCy) based graft-versus-host disease (GVHD) prophylaxis after mismatched unrelated donor (MMUD) hematopoietic cell transplant (HCT). Participants with malignant hematologic diseases eligible per inclusion criteria, receiving MMUD peripheral blood stem cells (PBSCs) after myeloablative conditioning (MAC) or reduced-intensity conditioning (RIC) will be eligible to be enrolled by participating transplant centers. The platform protocol will estimate endpoints and provide a comparator arm for investigational interventional arms (ISAs). Two investigational ISAs are part of the platform protocol - ACCEL-001 and ACCEL-002. The ISAs describe the specific features of the intervention being studied and treatment of participants assigned to that intervention, the specific target population, sample size required based on comparison to the control arm, specific study objectives, statistical methods for evaluating the interventions, and other specific intervention-related information and assessments. Additional ISAs may be added or closed throughout the lifetime of the trial.