This study consists of two phases, phase Ib and phase II. The primary objective of phase Ib is to evaluate the safety and tolerability of multiple doses of daratumumab in patients with refractory aplastic anemia. The primary objective of phase II is to preliminarily assess the efficacy of multiple doses of daratumumab in patients with refractory aplastic anemia. Secondary objectives include evaluation of other efficacy endpoints, safety (phase II), and pharmacodynamic characteristics of multiple doses of daratumumab in these patients. The exploratory objective is to assess biological functional changes in peripheral blood and bone marrow before and after daratumumab treatment.