I hope I understand your question and premise.
The P and S number materials listed in ASME exceed the limited number of materials listed in Table 3.1 of D1.1. If it is clear that you are referring the Table 3.1 "group 1" materials only, I do not see why you could not list it as group 1 to group 1 on a generic "Prequalified" AWS WPS. This would typically be used as an in shop WPS when there is no outside QC/QA or EOR surveillance.
However many "approving" entities (DOTs, States, Authorities, EORs, and other "approving authorities" for the contract, Etc.) often will want a very specific ASTM to ASTM and Product form to product form and Joint Detail to Joint Detail WPS for their project. Many require separate WPS's for each size of weld and type of joint. Some even require a diagram of exact bead placement.
If it is a WPS based on a qualified welding procedure, your options are more limited.
Each company has a way of accomplishing similar tasks using different means.
I have clients that have a separate WPS for each project, each process, and each weld joint. They have the WPSs in binders filed away under the project they were written for. The QC manager spends hours writing new WPS for each project.
Other clients do not have the same needs or the same system and have "general" WPSs that are adequate for the majority of the work they do.
The customer is usually the driving force that ultimately defines the type of system a contractor adopts. A subcontractor that works with several welding standards (invoked by their customer) may have several WPS for the same process, same base metal, but they are different because of the differences in the requirements of the applicable welding standard (or code).
Even welding performed to AWS may require different WPSs. Consider a company welding to the requirements of AWS D1.1 and D17.1. The numbering systems used to differentiate between the base metals are completely different. Groups I, II, III, and IV under AWS D1.1 are all steels. Group I is carbon steel, Group II is stainless steel, Group III is nickel, etc. if you are working to AWS D17.1.
Under ASME, a single material specification may contain several different P-numbered alloys. As an example, SB-626 includes P numbers P-43, P-44, and P-45. Within Section IX the alloys are differentiated by their UNS numbers and their P numbers.
As the individual responsible to develop the WPSs, you are tasked with the job of determining what system works best for your situation.
I get around the problem you mention by using an Annex attached to the WPS listing the material specification and as applicable, the grade, class, or UNS number. The WPS states P-XX joined to P-XX (or Group I joined to Group III) and under the heading of "Specification" I refer to the Annex. In the case of pipe, the specification and grade, class, or UNS is line stamped on the length, in the case of plate or sheet, the information is usually marked on the opposite corners. Listing the P, S, or Group numbers on the WPS serves little purpose to the welder because most welders do not understand the grouping of base metals and P, S, M, or Group numbers are not typically found stamped on the raw stock. Using my WPS, the welder simply looks at the Annex to "pull" the right material from stock based on the material specification and the grade, class, or UNS.
Good luck - Al
One thing that I do on my WPS's that seems to keep most people happy, yet maintain the flexibility of the WPS is have a statement similar to that below on the WPS under the base metal section:
"All AWS D1.1 Group I or II material welded to themselves or eachother, including, but not limited to the materals listed below:"
Then I list the most common ASTM specs, or the ones intended to be welded for a specific job, but the WPS is also not limited to the specific ASTM specs or job materials.
It has been my understanding that AWS prescribes few specific requirements for documentation. The codes says you must keep records. The code consists of numerous requirements. The code give sample forms, emphasis on sample.
Your WPS should be written in such a way that any welding that complies with your WPS should comply with the code. That in my opinion would be an acceptable WPS. If you get real loose on the parameters you specify on the WPS there is the possibility that someone could comply with your WPS while at the same time not complying with the code. That in my opinion would be an unsatisfactory WPS. You have to run through the 'traps' and anticipate how someone may misuse your WPS in a way not intented resulting in a code non-compliance.
This would be my general philosophy which would apply to base metals or anything else found on a WPS.