Study of Daratumumab for Decreasing Circulating Antibodies in Sensitized Patients Awaiting Heart Transplantation

Inclusion Criteria: * Participant is on an active list for a heart transplant. * Participant has a high level of allosensitization, defined as a calculated PRA (panel of reactive antibodies) of 50%, based on their antibody status at the time of entry into the study. * Ability to understand and willingness to sign an informed consent form prior to any study-related procedures. * Women of childbearing potential must have a negative pregnancy test at screening. * Both male and female patients must use effective methods of birth control, must not donate eggs or sperm during the course of the study and for 3 months after stopping daratumumab. Exclusion Criteria: * History of allergy or intolerance to daratumumab. * Prior diagnosis of myeloma or light chain amyloidosis. * Active infection. * Women who are pregnant or breastfeeding. * Ongoing desensitization treatment with another agent. Subjects are excluded if they have received: * a. IVIG within 30 days of enrollment. * b. Proteasome inhibitor within 60 days of enrollment. * c. Rituximab within 180 days of enrollment. * Any condition which could interfere with, or the treatment for which might interfere with, the conduct of the study or which would, in the opinion of the Investigator, unacceptably increase the subject's risk by participating in the study. * Contraindication to herpes zoster prophylaxis. * Known to be seropositive for human immunodeficiency virus (HIV). * Known to be seropositive for hepatitis B (defined by a positive test for hepatitis B surface antigen \[HBsAg\]). Subjects with resolved infection (ie, subjects who are HBsAg negative but positive for antibodies to hepatitis B core antigen \[anti-HBc\] and/or antibodies to hepatitis B surface antigen \[anti-HBs\]) must be screened using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus (HBV) DNA levels. Those who are PCR positive will be excluded. EXCEPTION: Subjects with serologic findings suggestive of HBV vaccination (anti-HBs positivity as the only serologic marker) AND a known history of prior HBV vaccination, do not need to be tested for HBV DNA by PCR. * Known to be seropositive for hepatitis C (except in the setting of a sustained virologic response (SVR), defined as aviremia at least 12 weeks after completion of antiviral therapy). * Known chronic obstructive pulmonary disease (COPD) with a forced expiratory volume in 1 second (FEV1) \<50% of predicted normal. Note that FEV1 testing is required for subjects suspected of having COPD and subjects must be excluded if FEV1 is \<50% of predicted normal. * Known moderate or severe persistent asthma within the past 2 years, or uncontrolled asthma of any classification.