Psoriatic arthritis (PsA) is a type of arthritis that happens when the body's immune system attacks healthy cells and tissues causing joint pain, stiffness, and swelling. Symptoms can get worse and go away for periods of time. This study will evaluate the efficacy and safety of targeted therapies through a series of substudies, for the treatment of active psoriatic arthritis and to assess the changes in disease symptoms. The therapies being assessed in this sub-study are risankizumab and lutikizumab. Participants will be randomized in a 1:1:1 ratio to one of the three treatment arms: lutikizumab monotherapy, risankizumab monotherapy or a combination therapy of lutikizumab and risankizumab. Around 120 participants will be enrolled in the study at approximately 40 sites worldwide. There may be higher treatment burden for participants in this trial compared to their standard of care (due to study procedures). Participants will attend regular visits during the study at a hospital or clinic. The effect of the treatment will be checked by medical assessments, blood tests, checking for side effects and completing questionnaires.