Hi Angela,
We have been a facing similar situation, where we had some introductory risk assessment questions, followed by a more comprehensive set of CSR questions. As Martin rightly points out, there can be only one SPQ, which logically makes sense.
The work-around that we have implemented was to simply add the comprehensive set of questions to the SPQ, then hide the view from the supplier and finally implementing them in our events template (visible). That way, Suppliers will be presented with the CSR questions at the right stage in the process, while the answers feed back into the SPQ, making you capable of reporting on them.
I hope this help you!