The goal of this long-term extension (LTE) study is to evaluate the safety and efficacy of pegtibatinase in patients with classical homocystinuria (HCU). Patients who are active in the Phase 1/2 COMPOSE study or those who complete the 24 weeks of treatment in the Phase 3 HARMONY are eligible to participate. Participants will be in this clinical study for up to about 13 months including: * a treatment period of up to 104 weeks * a 4-week safety follow-up period