[Varyon]

I've considered something like this in the past, and for more than just shotgun slugs, although I dismissed it assuming it wouldn't be as useful as I was hoping. The design would probably resemble the Hydra Shok, but with the center post made of tungsten carbide (or other armor penetrating material) that is weakly attached to the base, rather than formed from the bullet material. You need something designed to mushroom out, as otherwise the lead will probably go inward as well, likely trapping the penetrator. In theory, on impact the penetrator would detach, going deeper than the rest of the (hollow-point) bullet. In practice, however, I suspect the penetrator would be too light to go very deep at all, invalidating the design.

Assuming you can make the penetrator around half the weight of the rest of the round, and for simplicity we'll say it goes the entire length, the penetrator would have roughly half the kinetic energy (which scales linearly with mass) and 65% of the caliber of the round itself. If a non-expanding round of the same same size, density, and velocity would penetrate, say, 10 inches, the penetrator (going off of Douglas Cole's spreadsheet) would have 80% of the penetration of the non-expanding round. The expanding portion, meanwhile, would have half the kinetic energy but normal caliber, for 70% of the penetration. So, unless I'm misinterpreting things, against an unarmored target the weapon would function as a hollow-point round with 70% of normal damage, while against an armored one it would have 80% of the normal damage (and -1 to wounding class) of a solid round. Technically, the performance against an unarmored target would be a bit better than the above, as the penetrator would still do its damage - you'd be looking at 70% at +1 wounding class, 10% (80% minus 70%) at -1 wounding class; for 5d pi+, that's an average of 24.5 HP + 1.75 HP, or 26.25 HP, equal to the wounding from a solid slug. Honestly, considering the penetrator has less penetration than a solid slug, this means the design is invalid - against an unarmored target, it does no more wounding than a solid slug, and against an armored target, it has inferior penetration (and wounding, as most of the wounding character is eaten up by the armor) to a solid slug, unless I'm missing something (and I may be, I'm not certain exactly how Cole's spreadsheet handles armor-penetrating materials).

That said, at least in a cinematic setting, feel free to have this design function better. Something like 80% damage, and use the higher wounding of if the round were HP (+1 wounding class, AD (2)) or APHC (-1 wounding class, AD (2)). To work for a 12G shotgun, you'd need to allow for a pi+++ class (wounding modifier 2.5 or 3, up to you; we'll go with 3). So, a solid 12G shotgun slug is 5d pi++, an HP 12G shotgun slug is 5d (0.5) pi+++, an APHC 12G shotgun slug is 5d (2) pi+, and our bullet (we'll call it APDP, Armor Piercing Detached Penetrator) is the better of 4d (0.5) pi+++ and 4d (2) pi+.

Using 3.5 per die (technically, when DR comes into play this understates the average wounding a bit, as it effectively counts negative wounding results, but it's close enough), against a target with DR 0, a solid slug deals 35 HP wounding, an HP slug deals 49.5 HP wounding (remember, poor armor divisors mean -1 damage against unarmored foes), an APHC slug does 26.25 HP wounding, and an APDP slug does the better of 39 HP wounding (hollow-point) and 21 HP wounding; obviously, 39 is better. Against a foe with DR 5, these become 25 for solid, 22.5 for HP, 22.5 for APHC, and the better of 12 and 17.25 for APDP (17.25). Against a foe with DR 10, this is instead 15 HP for solid, 0 HP for HP, 18.75 HP for APHC, and the better of 0 and 13.5 for APDP (13.5). Note this still isn't great, but if you're expecting to go up against foes who have a mix of DR levels, it could be worthwhile as an all-around projectile. x2 cost (comparable to APHC) would be fair, x3 may be more likely (it's a fiddly round to produce).

Of course, for a really cinematic setting, just treat it as the better of HP and APHC.