Agreggate blog postings from users on a multi-site into the main site

I'm not sure if this is a simple or complicated issue, but I have a multi-site and I want to aggregate the blogs posts of the sites in the network into one feed. I also want to be able to filter the posts by category. This was the main reason I am setting up a multi-site so I hope it's possible!

Ideally, each user on the multi-site would have access to the same, shared categories. I have tried the Site Categories plugin but I don't it does what I need.

I am using the Parallax Framework with the Salutations theme on the main site, and all the other sites will use a variety of themes.