Wordpress Benefit to add page-cache (Fastest cache)

I have installed LEMP with option 22 with Redis at Nginx level, Redis Object Cache plugin and Nginx helper plugin in Wordpress. I'm considering to add a page-cache as well to get more options to for example be able to exclude some cookies from being cached.

Is this possible? Redis at any level is object-cache so having a page-cache should not be a problem?

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Ok, thanks for clearing that. Should I enable Cache Enabler also? There are some functionality that is good to have with that specific plugin.

 

Thank you! I'm just amazed by how you find time to answer all the questions!