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I have a small question that has got me thinking.

Is there a way for players to pick individual mutations in coop? I've been seeing all sorts of commands but can't find any that does that.

Or is it not an option? :o

Not at this time - adding such an option entails redesigning how mutations and related user interface (mutation picker screen and mutation lists) are handled on basic level. There might be mods that do this to some extent already - I'd suggest to ask around.