How to configure multiple FederationID values using SSO in Salesforce?

My client has asked to configure SSO using FederationID. When client login to the other application, they use either EmpID, userName, emailaddress for authenticating.

My issue is when client tries to log in to the salesforce, it expects only one value to enter while authentication. Client wants to login to the salesforce SSO using any value either EmpID, userName, emailaddress.