On-hit effects, which are different from on-hit abilities, do not apply an additional armor shred stack.
The very first instance of physical damage does not get the benefit of the armor reduction. The physical damage dealt is calculated first, and the debuff is applied after. This means the full benefit of the reduction is seen on the seventh hit, after all six stacks have been applied.
Armor reduction and penetration effects stack, allowing an attacking character to benefit simultaneously from Black Cleaver shred, penetration runes, other items such as Last Whisper, and champion abilities that circumvent armor.
When combined, The Black Cleaver and The Obsidian Cleaver will apply 2 stacks per instance of physical damage, instead of 1. This is because the unique passives are not named and they are not the same item. However, the two items share the same maximum stacks.
Multiple instances of physical damage applied at the same time (e.g. Zed'sRazor Shuriken with his shadow) will only apply one stack.
The Black Cleaver is usually used on juggernauts (Illaoi, Darius, Garen) because they can easily apply stacks and survive long enough to benefit from the penetration. Other than the shred effect they can also very nicely benefit from the bonus movement per hit which allows them to stick to their targets.
Building multiple Black Cleavers can be viable: with Transcendence and 40% CDR, The Black Cleaver grants 64 AD and 400 health, and is now worth:
Revised Passive: Dealing physical damage to an enemy champion Cleaves them, reducing their armor by 5% for 6 seconds, stacking up to 6 times.
The passive is now unique.
New Unique Passive:Rage: Dealing physical damage grants 20 movement speed for 2 seconds. Assists on Cleaved enemy champions or kills on any unit grant 60 movement speed for 2 seconds instead. This movement speed is halved for ranged champions.