1. The participant is aged 18 years or older at the time of signing the informed consent form (ICF). In South Korea, the age requirement for adult participants is \>=19 years of age.
2. The participant has completed the 52-week treatment period in one of the parent studies (TAK-279-PsA-3001 or TAK-279-PsA-3002) independent of treatment assignment, and without meeting the criteria for permanent discontinuation of trial intervention defined in the parent studies.
3. The participant must be deemed by the investigator to benefit from continued or newly initiated (that is, for participants randomized to active comparator in parent study TAK-279-PsA-3001) zasocitinib therapy.
You may not be if
1. Any participant who is deemed by the investigator to be not benefiting from the trial intervention based upon lack of improvement or worsening of their symptoms in the respective parent study.
2. Any participant who met the criteria for permanent discontinuation of trial intervention defined in the parent studies (TAK-279-PsA-3001 or TAK-279-PsA-3002).
3. The participant has developed any disease(s) that might confound the evaluations of benefit of zasocitinib therapy since enrollment in the respective parent study, including but not limited to rheumatoid arthritis, axial spondyloarthritis (this does not include a primary diagnosis of PsA with spondylitis), systemic lupus erythematosus, Lyme disease, gout, or fibromyalgia.
4. The participant has developed evidence of a concomitant comorbid skin condition that, in the opinion of the investigator, would interfere with the study assessments, such as evidence of non-plaque PsO (erythrodermic, pustular, predominately guttate PsO, inverse, or drug-induced PsO).
