Air Tag Tracked by Multiple iPhones

AirTags are associated with one Apple ID. Hopefully each and every person, regardless of age, has her/his own, unique Apple ID.

Set up your AirTag using your iPhone, iPad, or iPod touch - Apple Support

Based upon the OP's wording, it seems as if the answer is backwards from what they are asking. Can multiple people track one airtag? For example, an aging parent is always misplacing their purse. It would be good for the extended family which shares care taking duties to be able to find the purse.

An Airtag can only be associated and tracked by one Apple ID. If multiple people are sharing an Apple ID (REALLY BAD idea), then, theoretically, they call all track the Airtag.