The system is designed to allow a single Director to act for multiple companies or be associated with multiple. 

All you would need to do is link them together, which you would do by locating the LTD required, then adding the Director via 'Related Individuals and Contacts' 

Head to the Client - Section 2 - Add

If they're already in Engager, use the 'find existing individual Engager.app database' option and then DONE

Your Director should now sit under the 'related clients' in your overview of Clients

Once they're linked, the Director can now access ALL LTDs via the Portal, without having to maintain multiple logins / passwords etc.