Part 1 Inclusion Criteria: * The subject's legal guardian(s) is (are) willing and able to provide written, signed informed consent after the nature of the study has been explained, and prior to any research-related procedures * Is a male ≥4 months to \< 5 years of age on Day 1 * Must meet any of the following criteria: * Has a documented diagnosis of MPS II and a has a neurocognitive testing score ≤ 77 (Bayley or Kaufman), OR * Has a documented diagnosis of MPS II AND has a decline of ≥ 1 standard deviation on serial neurocognitive testing administered between 3 to 36 months apart (Bayley or Kaufman) OR * Has a relative clinically diagnosed with severe MPS II who has the same IDS mutation as the subject AND in the opinion of a geneticist has inherited a severe form of MPS II OR * Has documented mutation (s) in IDS that in the opinion of a geneticist is always known to result in a neuronopathic phenotype AND in the opinion of a clinician has a severe form of MPS II Part 2 Inclusion Criteria: * The subject's legal guardian(s) is (are) willing and able to provide written, signed informed consent after the nature of the study has been explained, and prior to any research-related procedures * Is a male ≥4 months to \< 5 years of age on Day 1 * Has a documented diagnosis of neuronopathic MPS II. Neuronopathic MPS II can be documented with any of the following methods: * Has a BSID-III Cognitive Composite score at or below -1 SD (85) from normative mean * Has two consecutive neurodevelopmental assessments that support a decline on MSEL visual receptive, expressive language, or fine motor, or BSID-III cognition, expressive language, or fine motor ≥ 1 SD on serial neurocognitive testing administered between 3 to 36 months apart * Has a relative clinically diagnosed with neuronopathic MPS II who has the same IDS mutation as the subject AND the subject, in the opinion of a geneticist, has inherited a neuronopathic form of MPS II * Has documented mutation(s) in IDS known to result in a neuronopathic phenotype Part 1 Exclusion Criteria: * Has contraindications for intracisternal (IC) injection, intracerebroventricular (ICV) injection or lumbar puncture * Has contraindications for immunosuppressive therapy * Has neurocognitive deficit not attributable to MPS II or diagnosis of a neuropsychiatric condition * Has a (cerebral) ventricular shunt that may impact the proper dosing of the subject * Received hematopoietic stem cell transplantation * Has had prior treatment with an AAV-based gene therapy product * Received ELAPRASE® via intrathecal (IT) administration within 4 months of signing the ICF or experienced a serious hypersensitivity reaction to ELAPRASE® * Has received any investigational product within 30 days of Day 1 or 5 half-lives before signing the ICF, whichever is longer Part 2 Exclusion Criteria: * Has a contraindication for an IC injection, ICV injection or lumbar puncture * Has contraindications for immunosuppressive therapy * Has neurocognitive deficit not attributable to MPS II or diagnosis of a neuropsychiatric condition * Has a (cerebral) ventricular shunt that may impact the proper dosing of the subject * Received hematopoietic stem cell transplantation * Has had prior treatment with an AAV-based gene therapy product * Is receiving idursulfase (ELAPRASE®) via intrathecal (IT) administration, or a blood brain barrier-crossing enzyme replacement therapy. Subjects receiving IT ELAPRASE® or a blood brain barrier-crossing ERT may enroll if they agree to discontinue these therapies starting at least 3 months prior to dosing with RGX-121, and for the 24 months of follow-up * Has received any investigational product within 30 days of Day 1 or 5 half-lives before signing the ICF, whichever is longer