The U.S. Census Bureau assigns and maintains only one NAICS code for each establishment based on its primary activity (generally the activity that generates the most revenue for the establishment). Since other federal government agencies, trade associations, and regulation boards maintain their own lists of business establishments and assign classification codes based on their own programmatic needs, this will vary by agency.
Yes, some agencies assign more than one NAICS codes to one establishment. For instance, the SAM (System for Award Management formerly CCR), where businesses register to become federal contractors, will accept up to 5 or 10 classification codes per establishment. You will need to contact the other agencies to find out what their policies are. For access to a list of federal government agencies, click here.