Can Black Cleaver get more Armor shred if it's worded to not function alongside Last Whisper?

The Black Cleaver

Phage (1250) + Kindlegem (800) + 950 = 3000

+400 Health +40 Attack Damage +20% Cooldown Reduction

Unique Passive - Strip Away: Dealing Physical Damage to an enemy champion reduces their Armor by 5% for 6 seconds, stacking up to six times for a maximum 30% Armor reduction. Disables Strike Through on your other items.

Unique Passive - Rage: Dealing Physical Damage grants 30 Movement Speed for 2 seconds. Takedowns on enemy champions or kills on other units grant 90 Movement Speed for 2 seconds instead. The Movement Speed bonuses are reduced by 60% on ranged champions (to 10 and 30 respectively).

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Last Whisper / Lord Dominik's Regards / Mortal Reminder: Unique Passive name changed to Strike Through.

Basically increased the Armor shred, added a clause that prevents said shred from working alongside Last Whisper, and increased Rage's movement speed on melee champions (the ranged penalty being upped to 60% from halved keeps the numbers the same as on live Rage).

It's like how the Dissonance passive on Athene's negates the Harmony passive on Mikael's. (Though I'm not entirely sure why Dissonance has to negate Harmony from a balance perspective. Would it really be too strong if they coexisted? I guess the combination of more AP for scaling heals and more Health Regen would make people like Soraka too durable? I dunno.)

The bit about the passive names is just because I wanted them to sound contradictory (like Harmony and Dissonance on Grail and Mikael's) and still be fitting to the items they're on, and I don't know what the opposite of "Last Whisper" would be that would sound fitting on a big ol' axe.

I'm sure you might have to tone back some of the other anti-tank measures if you buff Cleaver's shred (that means you, Darius E), but really, Cleaver kinda sucks on a lot of its intended users at the moment. Boosting the MS it gives melees via Rage is mainly to offset the fact that Trinity gives MS outright on top of its own Rage.