⁃ Part A:

• Participant is willing and able to understand and fully comply with study procedures and requirements (including digital tools and applications), in the opinion of the investigator.

• Participant has provided written informed consent and any required privacy authorization before the initiation of any study procedures.

• Participant is aged 18 years or older at the time of consent.

• Participant has a diagnosis of chronic plaque psoriasis for \>=6 months prior to the screening visit.

• Participant has stable plaque psoriasis defined as no significant flare or change in morphology (as assessed by the investigator) in psoriasis for \>=6 months before screening.

• Participant has moderate-to-severe plaque psoriasis as defined by a PASI score \>=12 and a sPGA score \>=3 at screening and Day 1.

• Participant has plaque psoriasis covering \>=10% of his or her total BSA at screening and Day 1.

• Participant must be a candidate for phototherapy or systemic therapy.

⁃ Part B:

⁃ \- Participant has completed 52 weeks of treatment (TAK-279-3001 or Part A) or 60 weeks of treatment (TAK-279-3002), or 16 weeks of treatment (TAK-279-PsO-3004) in their parent study.