Daratumumab in HLA Desensitization Prior to Transplantation

General Inclusion Criteria: * Absolute neutrophil count \> 1,500 * Total bilirubin \< 1.5x institutional upper limit normal (ULN) * AST/ALT \< 2. 5 - 3x ULN (Options for patients with liver dysfunction may be available) * Creatinine clearance \> 20 ml/min Specific Inclusion Criteria \[HLA Desensitization Group\] * Calculated PRA (cPRA) greater than 50%. * Currently actively listed for heart or combined heart and kidney transplantation. * Negative pregnancy test (if woman of childbearing potential) If able to become pregnant or father a child, agreement to use one of the birth control methods described in this protocol * Able to provide informed consent General Exclusion Criteria: * Prior or current exposure to any of the following: daratumumab or other anti-CD-38 therapies, exposure to an investigational drug (including investigational vaccine) or invasive investigational medical device for any indication within 4 weeks or 5 pharmacokinetic half-lives, whichever is longer. * 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 participants suspected of having COPD and participants must be excluded if FEV1 is \< 50% of predicted normal. * Moderate or severe persistent asthma within the past 2 years, or uncontrolled asthma of any classification. Note that participants who currently have controlled intermittent asthma or controlled mild persistent asthma are allowed to participate. * Woman who is pregnant or breastfeeding. Participant is: known history of human immunodeficiency virus (HIV); Seropositive for hepatitis B (defined by a positive test for hepatitis B surface antigen \[HBsAg\]). Subjects with resolved infection (i.e., subjects who are HBsAg negative with antibodies to total hepatitis B core antigen \[anti-HBc\] with or without the presence of hepatitis B surface antibody \[anti-HBs\]) must be screed 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 HBV vaccination, do not need to be testing for HBV DNA by PCR; 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). Clinically significant cardiac disease, including: myocardial infarction within 6 months before randomization, or unstable or uncontrolled disease/condition related to or affection cardiac function (e.g., unstable angina, congestive heart failure, New York Heart Association Class III-IV); Uncontrolled cardiac arrhythmia Specific Exclusion Criteria \[HLA Desensitization Group\] * Patients listed for combined heart and liver transplantation will be excluded, as our unique experience with combined heart liver transplant (liver placed first), has demonstrated that in those cases high levels of circulating HLA antibodies may not increase the risk of hyperacute rejection. * Seropositivity for human immunodeficiency virus (HIV) * Seropositivity 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. * Seropositivity 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). * Patients unable to give informed consent will also be excluded.