Aggregate blog posts from other blogs onto one main blog

OK, I know that this has been asked before, but I’ve got a different twist and I’m not quite sure how to go about doing this. What I want to do is have a number of blogs that will be hosted on either different subdomains or possibly different domains alltogether. I then want to have all of the posts from those different blogs pulled into one main blog that is on a different domain alltogether. For example, let’s say that I have blog1.mydomain.com, blog2.mydomain.com, blog3.mydomain.com, and blog4.com and I want to be able to post different things on those blogs but then have those posts show up on https://www.mydomain.com.

Each different domain or subdomain will basically be a different category on the main blog (www.mydomain.com). Beyond just haveing each post on the subdomains show up on the main blog, I want to be able to give logged-in users the option to only show certain categories on the home page. Is there a plugin that will allow logged-in users to only display certain categories on the front page? Thanks in advance for your responses.