Google has a limit to how long searches can be. So if it’s a complex one, it can’t be too long.

I think you can only specify searching one site at a time. With site: search filter.

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Google’s custom search engine’s where you can give a whitelisted amount of sites isn’t very good. At least not any more. It didn’t include lots of pages it’s main index does. Or the rankings were all out of sorts rendering not useful.