Background: Blood cancers (such as leukemias or lymphomas) often do not respond to standard treatments. A transplant of blood stem cells from a healthy donor can help people with these cancers. Sometimes these transplants cause serious side effects, including a common immunologic problem called graft-versus-host disease. A drug called cyclophosphamide given early after the transplant (post-transplantation cyclophosphamide, PTCy) can reduce these complications. But sometimes this drug has its own negative effects. Furthermore, studies in mice suggest that an intermediate, rather than very high, dose of this drug may best protect against graft-versus-host disease.

Objective: To find out if a lower dose of PTCy is more helpful for people who undergo blood stem cell transplants.

Eligibility: People aged 18 and older who have a blood cancer and are eligible for a transplant of blood stem cells from another person. Healthy donors are also needed but must be related to the individual needing the transplant.

Design: Participants will undergo screening. Transplant recipients will have imaging scans and tests of their heart and lung function. They will be assessed for the status of their cancer, including bone marrow taken from their pelvis and possibly also scans and/or fluid drawn from the spine depending on the disease type. Donors will be screened for general health. They will give several tubes of blood. They will give an oral swab and saliva and stool samples for research. Recipients will be in the hospital at least 4 to 6 weeks. They will have a temporary catheter inserted into a vein in the chest or neck. Medications will be given and blood will be drawn through the catheter. The transplanted stem cells will be given through the catheter. Participants will receive medications both before and after the transplant. Participants will return to the clinic at least once a week for 3 months after leaving the hospital. Follow-up visits will continue periodically for 5 years.