A Study to Evaluate the Efficacy and Safety/Tolerability of Subcutaneous MK-3222 in Participants With Moderate-to-Severe Chronic Plaque Psoriasis (MK-3222-012)

Inclusion Criteria * Clinical diagnosis of moderate-to-severe plaque psoriasis for at least 6 months prior to enrollment; * Candidate for phototherapy or systemic therapy; * Premenopausal female participants must agree to abstain from heterosexual activity or use a medically approved method of contraception or use appropriate effective contraception as per local regulations or guidelines * For the extension study: must have completed Part 2 of the base study * For the extension study: must have achieved at least a PASI-50 response by the end of Part 2 of the base study Exclusion Criteria: * Non-plaque forms of psoriasis * Presence or history of severe psoriatic arthritis that is well-controlled on current treatment regimen * Women of childbearing potential that are pregnant, intend to become pregnant, or are lactating * Participant is expected to require topical therapy, phototherapy, or systemic therapy * Presence of any infection or history of recurrent infection requiring treatment with systemic antibiotics * Previous use of MK-3222/SCH 900222, or other interleukin-23 (IL-23)/T- helper cell 17 (Th-17) pathway inhibitors including P40, P19, and IL-17 antagonists, or etanercept * Latex allergy or sensitivity * Active or untreated latent tuberculosis (TB) * For the extension study: women of child-bearing potential that are pregnant, intend to become pregnant within 6 months of completing the trial, or that are breast feeding * For the extension study: active or uncontrolle…