This clinical trial is for adult participants who have primary antiphospholipid syndrome (APS). APS is a rare and chronic autoimmune disorder, meaning that it occurs when the body's immune system mistakenly attacks healthy tissues and organs. APS is common in patients with other autoimmune or rheumatic diseases, particularly systemic lupus erythematosus (SLE). APS is referred to as "primary" when it occurs alone. Participants in this study have been diagnosed with primary APS.
   
The purpose of this study is to see whether the study drug, daratumumab (Darzalex), is safe to treat primary antiphospholipid syndrome (APS). Currently, APS treatment is given to improve signs and symptoms and to prevent serious damage to the body. Research for a more effective treatment for APS is needed to keep the disease under better control, and perhaps avoid the need for life-long medications.
   
Daratumumab is a man-made antibody that works by targeting a protein called CD38, which is on the surface of multiple myeloma tumor cells as well as certain immune cells. In APS, daratumumab may work by eliminating the cells that produce antiphospholipid antibodies associated with damage to the body, for example blood clots, miscarriage or stillbirth. Daratumumab may also interfere with destructive immune cells resulting in APS becoming less active or even inactive.

Daratumumab is currently approved by the U.S. Food and Drug Administration (FDA) to treat a blood cancer called multiple myeloma. It is not approved to treat APS and is considered an experimental treatment.
   
Study participants will receive one of three different doses of daratumumab. The 16 mg/kg dose is approved for a type of cancer called multiple myeloma, but researchers do not know whether a lower dose may be as effective and/or have fewer side effects in APS. The study drug is given via intravenous (IV) infusion into a vein in the arm. The first infusion may take about 7 hours and may be split into 2 infusions over 2 days in a row. Future infusions may take about 3-5 hours to complete depending upon how the participant feels. The dose participants receive will depend on when they join the study:
   
   --The first group will be assigned to receive daratumumab 4 mg/kg once a week for 8 weeks. 
   --The second group will be assigned to receive daratumumab 8 mg/kg once a week for 8 weeks.
   --The third group will be assigned to receive daratumumab 16 mg/kg once a week for 8 weeks. 
   
Participation in this study will last approximately 48 weeks and will include approximately 15 study visits to the study center.