You need an additional table or two to manage what are actually many to many relationships. As I understand your description, any given Project record can be linked up to 10 Clients and to up to 10 companies. This indicates that any Project can be linked to many clients while any client can be linked to any project. The same can be said of Projects to Companies. I'll just focus on Clients to Projects, but the same needs to be done for Project to Companies as well:
Start with these relationships:
Projects::__pkProjectIDID = Project_Company::_fkProjectIDID
Companies::__pkCompanyIDID = Project_Company::_fkCompanyIDID
You can place a portal to Project_Company on the Projects layout to list and select a Companies record for each given Projects record. Fields from Companies can be included in the Portal to show additional info about each selected Companies record and the _fkCompanyIDID field can be set up with a value list for selecting Companies records by their ID field.
For an explanation of the notation that I am using, see the first post of: Common Forum Relationship and Field Notations Explained