o-3 visas are available to accompanying spouses and unmarried children under age 21 of o-1 or o-2 visa holders. o-3 visas allow relatives to remain in the u. s., but they may not work. They may seek permanent residence while in o-3 status.
Although people on 0-1 visas and their spouses and children on 0-3 visas are permitted to apply for permanent residence (a green card) while in nonimmigrant o status, this is not true of o-2s (support staff). They must have the intent to depart the U. S. and they must maintain a residence abroad during their U. S. stay.