The alloy is called UNS S30400.
Calling it anything else is a common name and subject to misinterpretation.
You can search ASTM specifications by UNS numbers.
To clarify: Type 304/UNS S30400 is a designation denoting a compositional spec only. This alloy is then specified under various ASTM specs serving different functions. ASTM specs are not the only ones to incorporate Type 304 of course.
But that is what he asked for.
S30400 is listed in 46 ASTM product specs (not general specs) that I found on first pass.
Once he knows his product form and application he can select the appropriate product spec.