You will get a variety of answers on this question because the code does not give hard fast rules on documentation. Also, I'm not sure what a "pqwp" is either.
In my opinion, if you write a preq. WPS for A36 to A36 then that preq. WPS can only be used for A36 to A36. However, you could write a preq. WPS for Group II to Group II, and that preq. WPS could be used for A36 (>3/4in.) to A36 (>3/4in.) as well as other Group II to Group II materials.
In short, you must follow the directions in your documentation. If your documentation limits you to A36 to A36 then that is what you must comply with, but there is nothing in AWS D1.1 that prohibits the putting more than one steel spec or even group numbers in the form for base materials. Be careful though, if you make your preq. WPS too broad then there is a greater possibility that someone could follow and comply with your preq. WPS but perform welding which is not considered prequalified in accordance with D1.1.