I don't think this is possible, it's simply beyond the protocol. The SP provides a service, the IdP is responsible for user authentication. There seems to be no place for a 3rd party service between the two.
I guess you control (at least) either the SP or the IdP. Try to implement your survey (or whatever) at the provider you control.
As an alternative, you could try to implement your own IdP including a survey (or whatever) that uses the original IdP for authentication.