Any complications in defining Contract employee real employer as legal employer in HCM Cloud

Hi,
We do have contract employees defined as CWK in our Cloud HCM application. We will need to manage their absences & other real HR data. But not running payroll for them. Contractors often switches from agency A to B on new contracts.
We are not very much comfortable with linking their records to our company name as Legal Employer.
My question is, can we define their agency names as legal employer in our system. like ABC Agency, & XYZ agency. This would give us the clear picture that their legal employer in reality is same as what is in system. In Organization tree, we will keep them under our Enterprise.