This randomized phase II trial studies the safety and how well multi-peptide cytomegalovirus (CMV)-modified vaccinia Ankara (MVA) vaccine works in reducing CMV complications in patients previously infected with CMV and are undergoing a donor hematopoietic cell transplant. CMV is a virus that may reproduce and cause disease and even death in patients with lowered immune systems, such as those undergoing a hematopoietic cell transplant. By placing 3 small pieces of CMV deoxyribonucleic acid (DNA) (the chemical form of genes) into a very safe, weakened virus called MVA, the multi-peptide CMV-MVA vaccine may be able to induce immunity (the ability to recognize and respond to an infection) to CMV. This may help to reduce both CMV complications and reduce the need for antiviral drugs in patients undergoing a donor hematopoietic cell transplant.