Central hypersomnia conditions are a group of sleeping disorders where the brain has trouble keeping a person awake during the day (called excessive daytime sleepiness or EDS). These conditions usually include narcolepsy (type 1 and 2) and idiopathic hypersomnia (IH). Narcolepsy type 1 (NT1) includes sudden muscle weakness while you stay awake, called cataplexy, often triggered by strong emotions. Narcolepsy type 2 (NT2) does not include cataplexy. People with narcolepsy typically feel refreshed by short naps. People with IH feel extremely sleepy during the day, and do not feel refreshed by sleep. Waking up from sleep is difficult. This is common in the morning and also when waking up from long naps.

The study wants to learn about TAK-360 when taken over a long time period; this is called a long-term extension or LTE study. The main aim of this LTE study is to find out how well participants with NT1, NT2, and IH tolerate TAK-360 over a longer period (long-term tolerability) and to learn how safe TAK-360 is when given over a longer period of time (long-term safety).

Participants who completed one of the TAK-360 parent studies can join this study if they meet the study rules. Parent studies include TAK-360-2001(NCT06952699), TAK-360-2002 (NCT06812078), or other TAK-360 studies that evaluate the TAK-360 medicine. All participants will receive TAK-360 in this study. They will either receive the same dose as they did in the parent study, or the closest dose available in this LTE study. Participants who received placebo (the placebo looks just like TAK-360 but does not have any medicine in it) in their parent study will receive one of the TAK-360 doses available in this study. Placebo will only be used to not reveal the dose of TAK-360 from parent studies to investigator, participants, and sponsor. Sponsor, investigators and participants will not know which TAK-360 dose was used in the LTE study as long as the parent study is ongoing.

The participants will have to visit the clinic multiple times during this study.

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.

Takeda provides access to the de-identified individual participant data (IPD) for eligible studies to aid qualified researchers in addressing legitimate scientific objectives (Takeda's data sharing commitment is available on https://clinicaltrials.takeda.com/takedas-commitment?commitment=5). These IPDs will be provided in a secure research environment following approval of a data sharing request, and under the terms of a data sharing agreement.

IPD from eligible studies will be shared with qualified researchers according to the criteria and process described on https://vivli.org/ourmember/takeda/. For approved requests, the researchers will be provided access to anonymized data (to respect patient privacy in line with applicable laws and regulations) and with information necessary to address the research objectives under the terms of a data sharing agreement.