A Study of TAK-360 in People With Narcolepsy or Idiopathic Hypersomnia

Key Inclusion Criteria: 1. Participant is willing and able to understand and fully comply with trial procedures and requirements. 2. Participant has a confirmed diagnosis of either NT1, NT2, or IH, and has completed the treatment period of a parent TAK-360 trial. 3. Participant has provided informed consent (that is, in writing, documented via a signed and dated informed consent form (ICF) and any required privacy authorization before the initiation of any trial procedures. Key Exclusion Criteria: 1. Participant has a positive pregnancy test or is lactating/breastfeeding. 2. Participant has a risk of suicide according to endorsement of item 4 or 5 on the Columbia Suicide Severity Rating Scale (C-SSRS). 3. The participant has developed a new medical disorder associated with excessive daytime sleep (EDS). 4. Participant has developed (within the last 6 months) gastrointestinal disease that is expected to influence the absorption of drugs. 5. Participant has developed a new history of seizures. 6. Participant has experienced clinically significant head injury, per investigator opinion. 7. Participant has developed a history of cerebral ischemia, transient ischemic attack (less than \[\<\] 5 years ago), or cerebral haemorrhage. 8. Participant has developed a history of myocardial infarction, clinically significant coronary artery disease, clinically significant angina, clinically significant cardiac rhythm abnormality, or heart failure. 9. The participant has been diagnosed with medically significant thyroid disease, known functional hepatic impairment, or other severe chronic medical condition other than the central hypersomnolence disorder. 10. Participant has developed a history of cancer in the past 5 years.