I believe you’d need to modify user roles on each site individually (if I’m understanding your question correctly).
There’s a great plugin I use frequently called WPFront User Role Editor that allows you to check/uncheck user capabilities like you mentioned. The free version should be fine for what you’re trying to do. I personally use the paid version just because I like to have the extra options when I need them, but 90% of the time the free one works fine.
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