Pegtibatinase as a Treatment for Participants With Classical Homocystinuria (HCU) Receiving Standard of Care Treatment

Primary Objective: Researchers want to learn more about how pegtibatinase will affect homocysteine and methionine levels when it is injected under the skin in participants already receiving standard treatment. Blood tests will be used to measure changes in these levels during the study. Secondary Objectives: Researchers also want to learn: * Is pegtibatinase safe and tolerable (how does it make participants feel)? * How does pegtibatinase move throughout the body? * Does pegtibatinase produce antibodies (proteins the body makes that may stop pegtibatinase from working or cause side effects)? * How does pegtibatinase affect daily lives of participants with HCU? Researchers will use blood tests, urine tests, physical examinations, and questionnaires to answer these questions. Study Population and Treatments: This is a global study will include children and adults from 12 to 65 years old. Participants in the study will take their standard of care treatment. Participants will be put into 1 of 2 groups at random (like the flip of a coin) to take either: * pegtibatinase, or * an injection that does not have any medicine in it (or "placebo"). These are given as injections under the skin 2 times a week for up to 24 weeks. Neither the researchers nor the participant knows which treatment they are getting until the study is complete. Study Duration and Visits: Participants may be in the study for up to 38 weeks, including the screening period of up to 4 weeks, a pre-treatment period of up to 6 weeks where the participants will discuss their current diet with a dietitian (a health professional specialized in nutrition), a blinded treatment period of up to 24 weeks, and a safety follow-up visit completed 4 weeks after the last dose of study medication. Participants who complete the blinded treatment period may qualify to join the ENSEMBLE study before finishing the safety follow-up visit. Participants who meet all study requirements may have up to 58 study visits. Visits may take place at a study center, at home, or by telemedicine. These visits can include: * Blood and urine tests * Physical examinations * Questionnaires * Injections * Questions about how they are feeling or any problems they are having Safety / Adverse Events: Researchers will monitor participants for any medical problems that occur during the study. Participants will have regular laboratory tests, health checkups, and study visits to monitor their health and safety. Benefit-risk Conclusion: Researchers have worked to reduce risks to participants in this study. They believe the risks of taking pegtibatinase in this study are justified by the potential benefits that they think pegtibatinase may have for people with HCU.