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 study will evaluate the safety, tolerability, and efficacy of Orca-T in participants undergoing reduced intensity or non-myeloablative allogeneic hematopoietic cell transplantation (alloHCT) for hematologic malignancies. Orca-T is an allogeneic stem cell and T-cell immunotherapy biologic manufactured for each patient (transplant recipient) from the mobilized peripheral blood of a specific, unique donor. It is composed of purified hematopoietic stem and progenitor cells (HSPCs), purified regulatory T cells (Tregs), and conventional T cells (Tcons).