1\. The participant has completed TAK-079-3002 (end of trial \[EOT\]) or TAK-079-1004 (EOT). Participants from TAK-079-1004 must have had a response to mezagitamab as demonstrated by meeting the criteria for "platelet response" specified for that trial during either the main study or open-label extension.
For TAK-079-3002 participants:
1\. The participant has a history of severe allergic or anaphylactic reactions to recombinant proteins or excipients used in the mezagitamab formulation.
For TAK-079-1004 participants:
1. The participant has had any thrombotic or embolic event within 12 months before signing the ICF.
2. The participant has had a splenectomy within 3 months before signing the ICF.
3. The participant has active infection with hepatitis B virus (HBV), hepatitis C virus (HCV), or human immunodeficiency virus (HIV).
4. History of malignancy (including myelodysplastic syndrome) within 5 years of signing the ICF, except for treated non-melanoma skin cancer or cervical carcinoma in situ.
5. In the opinion of the investigator, the participant has a serious medical or psychiatric illness that could potentially interfere with the completion of treatment according to this protocol.
6. The participant has received anti-cluster of differentiation (CD) 20 treatment within 12 months before screening and either of the following applies:
1. The last dose was received within 6 months before screening.
2. The last dose was received between 6 and 12 months before screening and the participant has a CD19+ count below the lower limit of normal.
7. The participant has received any monoclonal or polyclonal antibody for immunomodulation within 6 months before Visit 1.
8. The participant has been exposed to another investigational agent within 4 weeks or 5 half-lives, whichever is longer, before Visit 1.
9. The participant has used anticoagulants (for example, vitamin K antagonists, direct oral anticoagulants) within 3 weeks prior to Visit 1.
10 The participant has received a live or live-attenuated vaccine within 4 weeks prior to the first dose of trial treatment or has any live or live-attenuated vaccine planned during the trial.
11\. The participant has used the following immunosuppressive agents as specified prior to Visit 1: alkylating agents (for example, cyclophosphamide) within 8 weeks, vinca alkaloids (for example, vincristine) within 4 weeks, sulfones (for example, dapsone) within 3 weeks, antiproliferative agents: (for example, mycophenolate mofetil and azathioprine) within 2 weeks, and calcineurin inhibitors: (for example, cyclosporine) within 2 weeks.
12\. The participant has a history of severe allergic or anaphylactic reactions to recombinant proteins or excipients used in the mezagitamab formulation.
Other protocol defined inclusion/exclusion criteria may apply.