There are a few similar material references that you may be able to find. In addition to AISI you will find cast type 316 Stainless Steel references as ASTM A351 Grade CF8M or ASME SA351 Grade CF8M. CF8M is listed as UNS S31600. You may also find ASTM A743-CF8M, F316L-CF8M.
Metengr mentions specific applications. Some valves and fittings are suitable in cast type 316 stainless steel and other pressure containing components may require forgings.
One thing to watch out for is that CF8M will typically have higher ferrite than 316 wrought material. Depending on your use, this can be detremental or beneficial, but if you are having CF8M made to order, you can specify ferrite percent to your own needs.