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So my laptop only meets minimum requirements and ingame settings don't offer much. Is there any way to tone down the graphics settings (v-sync, ffaa, texture qualtiy, post-process etc.) to make it more playable?

I checked C:\Users\...\AppData\LocalLow\Nightdive Studios\System Shock but there is no config file inside that folder I could poke through :/ Nothing in game install folder either as far as I can see.
Adjust settings in game? Drop your resolution and see how it runs.