One must qualify the WPS (per AWS D1.1 Structural Welding Code) that is used to weld an unlisted base metal to itself, to another unlisted base metal, or to a listed base metal. The qualified WPS is only valid for the the specific base metal specifications and grades used to qualify the WPS.
Example:
B.M. ABC welded to ASTM A572 Gr 50; since ABC is an unlisted B.M., the WPS is only qualified and valid for that specific combination, i.e., B.M. ABC to ASTM A572 Gr 50.
This is different than a WPS that is qualified using two listed base metal specifications where the WPS is generally qualified for the base metals included in the grouping.
Best regards - Al