A Study of TAK-279 in Adult Participants With Generalized Pustular Psoriasis or Erythrodermic Psoriasis

The main aim of this study is to check if TAK-279 improves symptoms of With Generalized Pustular Psoriasis (GPP) or Erythrodermic Psoriasis (EP) and side effect from the study treatment or TAK-279. All participants will be assigned to study treatments of TAK-279 and will be treated with TAK-279 if the participants meet the study rules. Participants will be in the study for up to 61 weeks including 52 weeks of study treatment. During the study, participants will visit their study clinic for multiple times.

Inclusion Criteria: 1. A diagnosis of GPP or EP prior to the screening visit. 2. Candidate for phototherapy or systemic therapy. Exclusion Criteria: 1. Other forms of psoriasis. 2. History of recent infection. 3. Any prior exposure to TAK-279, or participation in any study that included a TYK2 inhibitor. Other protocol defined inclusion/exclusion criteria apply.