LOL at "armor-piercing shotgun slugs"
12 gauge shotgun slugs are the opposite of what makes a good armor-piercing projectile. They are relatively big (large frontal area) and relatively slow. For piercing armor, a small diameter, pointy projectile (such as a spitzer bullet), at high velocity works best, for reasons which should be obvious. This is why typical soft body armor such as IIIA will stop typical handgun and shotgun rounds, including 12 gauge slugs, but typical rifle rounds go through them like a hot knife through butter.
Ironically, there's a common-as-dirt cartridge that's far more effective against body armor than 12 gauge slugs, i.e., 5.56 NATO (which is the standard cartridge for the equally common AR-15/M16 rifle platform). Any armor that can stop 5.56 NATO will inherently stop a 12 gauge slug, even if the slug is steel rather than lead, with ease.
There's no such thing as soft body armor that can stop 5.56 NATO. In order to stop it you need thick, hard plates made of steel or ceramic (III+ at a minimum, and that's only against non-AP rounds; the best 5.56 NATO AP rounds [tungsten core, e.g., M995 AP4] will defeat even level IV if the barrel is long enough), and in practical terms, those can only be worn on the front and rear of your torso. If you tried covering your arms, shoulders, legs, pelvic region, and neck with them, you'd have next to zero mobility.
If the movie makers had asked someone who knew what they were talking about, instead of their secretary, when Wick's character asked for something more effective against armor, he would have been given something that can easily defeat any body armor in existence, including level IV, such as the 7.62 NATO M948 SLAP round.