I recently purchased a used P320RX full size. I have a Carry with the Compact and Subcompact Kits. All are 9x19mm.

Three 17-round magazines refuse to lock into the full size grip module; however, they work okay on the Carry, Compact, and Subcompact grip modules.

Five other 17-round magazines, that look identical to the other three, lock into the grip module on all four sizes.

Any one got an idea as to why this is happening?

Not the old mag base types that won't fully insert into the x-frames are they?

Even though you said all the magazines look the same, my first thought was also about the floor plates.

I’d remove the floor plates from the problem magazines and try inserting them that way.
If the mag tubes by themselves seat and lock okay, then switch the floor plates from the mags that work onto the ones that don’t.

Added: What’s odd is that the problem mags fit in the Carry grip module. The Carry uses the same magazines as the full size module, so I suspect it must be some incompatibility between module and floor plates. Does your pistol have the X grip module?

SIGfreund was right.

I do not have an X-grip module; however, the three magazines that came with the Carry have plates marked "SIG" (and which don't work in the full size grip module) whereas the others say "SIG Sauer."

It looks like a bit of sanding on the baseplates may offer the solution.

I'll do some pictures later and update with visuals.