Primary immune thrombocytopenia (ITP) is a condition where the immune system mistakenly destroys platelets, which are cells that help stop bleeding. This leads to a lower number of platelets, making it easier to bruise or bleed. The main aim of this study is to check how safe mezagitamab is and how well it is tolerated by adults with chronic primary ITP, if given over a longer time. Other aims are to learn how effective treatment with mezagitamab is and how the body processes it (called pharmacokinetics or PK) over a longer time. Participants of the following previous mezagitamab studies will be invited to join this continuation study: TAK-079-3002 and TAK-079-1004. In this continuation study, participants will receive mezagitamab when certain protocol criteria are met. During the study, participants will visit their study clinic several times.