Final answer:
Detaining a person for an additional 24 hours without a court order is not allowable within the specified time period for involuntary examination.
Step-by-step explanation:
Within the specified time period for involuntary examination, the action not allowable based on the individual needs of the person being detained is detaining the person for an additional 24 hours without a court order. In cases of involuntary examination, the options typically include petitioning for involuntary placement, releasing the person for outpatient treatment, or releasing the person entirely if it's deemed appropriate. However, extending the detainment without court authorization generally violates the person's legal rights, particularly the writ of habeas corpus, which demands that a person detained by the authorities is entitled to have the validity of the detention reviewed by a court. The referenced cases, such as Vignera v. New York, Westover v. United States, and California v. Stewart, highlight the importance of the notification of rights during interrogation, which is a related issue concerning legal protections during the detainment of individuals.