It is only possible to add 2 contacts for access to the portal.

You can create a client file for the 3rd or 4th director. If you navigate to Clients > New Client and enter them using the Self Assessment Client Type, (if you do not actually do their self assessment then do not turn the self assessment service on). Once this client file has been created you can use the Client Link tab to link this person to the company or partnership.

You can then invite this person to register for portal access, they will not have the company/partnership to view but this will allow you to upload documents for them to sign.