It has a bunch of meanings!
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quite literally, this CEO has been locked in an elevator made of steel plate and plexiglass, with no way out
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cybernetics are often visualized in Cyberpunk as gleaming metal and smooth, glossy plastic. “Every damn line I hock at these jocks got ‘em locked in a heap of plastic and plate” is a reference to overcoming the overwhelming strength and power of a corpo-cyborg-militia through subterfuge, hacking, and clever manipulation. If you shut down a cyborg’s robotic components, they’d be helpless, weighed down by their non-functional body parts.
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plastic and plate metal are both evocative of industry, to me. At the end, suggesting that the CEO will “take ‘til [his] heart is plastic and plate” is saying that he’ll keep amassing power and wealth at the expense of others until capitalism devours his heart completely, removing his humanity.