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Say I have Major Shockwave with 2 LV Gamma-Disruptor Launchers, and I try to play a third copy onto him. Would the two already on him both scrap, or would only one?

You would have to scrap only one of the two LV Gamma-Disruptos Launchers already on Major Shockwave.
Source: Wizards of the Coast (2019-06-07)    【Link to Ruling】
Tags: LV Gamma-Disruptor Launcher