Key Inclusion Criteria: * Confirmed diagnosis of Wilson disease based on genetic confirmation of heterozygous or homozygous biallelic ATP7B mutation. * Stable Wilson disease as evidenced by ongoing copper chelator (ie, penicillamine, trientine) and/or zinc therapy for at least 2 months at screening, with no medication or dose changes for at least 2 months at screening. * Ongoing restriction of high copper containing foods for at least 2 months at Screening and continued through study participation. * Willing and able to comply with all study procedures and requirements, including frequent blood collection, total urine collection over a 24-hour period, patient-reported outcome assessments, and long-term follow-up Key Exclusion Criteria: * Detectable pre-existing antibodies to the AAV9 capsid. * Stage 1 only: History of copper chelator or zinc therapy noncompliance, in the Investigator's judgment, within 6 months prior to Screening. * History of liver transplant. * Active decompensated hepatic cirrhosis or history of hepatic encephalopathy. * Significant hepatic inflammation as evidenced by laboratory abnormalities. * Model for End-Stage Liver Disease (MELD) score \> 13. * Hemoglobin \< 9 g/dL * Presence of Stage 3 or higher chronic kidney disease based on estimated glomerular filtration rate \< 60 mL/min/1.73 m2. * Marked neurological deficit or compromise that, in the Investigator's opinion, would interfere with the subject's safety or ability to participate in the study. * Moderate to severe depression, recent or active suicidal ideation with intent or suicidal behavior, psychosis, or unstable psychiatric illness. * Known hypersensitivity to UX701 or its excipients, copper chelators, zinc, rituximab, tacrolimus, corticosteroids, or eculizumab that, in the Investigator's judgement, places the participant at increased risk for adverse events. * Participation in another gene transfer study or use of another gene transfer product before or during study participation. * Subjects with known hypersensitivity to amide-containing local anesthetics are excluded from participating in the optional liver biopsy substudy. Note: Other protocol defined Inclusion/ Exclusion criteria may apply