I’m looking to buy a few P320 compact mags for my X-gripped compact model, but I know the old mags with the “wings” for the traditional grip don’t fit. Is there a new part number for the mags with the new baseplates?

No, they use the same part number.

Your best bet is to email the seller and have them ensure that the mags they send you are the new style with the newer basepads. The new basepads still have wings, but they're thin enough to slide inside the bottom of the grip module.

However, if you have (or receive) some mags with the older baseplates, you can convert them in a minute or so with a pair of side-cutting nips and some sandpaper. You simply have to snip off the vertical wings and then sand down any remaining jagged areas.

You want mags with the Sig oval logo on the bottom & not the ones spelling out Sig Sauer.

A simple way to determine is to ask if the baseplates have a round or square retaining hole in the bottom, and/or if the basepads say SIG or Sig Sauer.

The newer style will have a square retainer and say SIG (top image).

The older style will have a round retainer with Sig Sauer (bottom).

As noted above, if you clip off the dog ears on the mags, it doesn't make any difference which mag you use.

If you run a 17 round magazine in a 15 round gun, it doesn't make any difference either, because the grips won't interfere. If you're running an x-cmpact with 15 round magazines, using 17 round magazines places the dogears outside the mag well, so it doesn't matter which style basepad you have.

For a 15 round magazine, the new style with the square peg on the baseplate will work fine, and if it's the older style with the round peg, just clip off the dog ears on the baseplate and you're good to go. It takes a few seconds to do, and you don't even need to sandpaper it if you don't want to, because it's purely cosmetic.