You can copy and paste content into your own blogs. No problem
The big problem is Google is not going to rank your blog.
For Eg - if you are running news blogs and there's enough original commentary or some sort of original content in your blog, then you can get away with quite a bit of “syndication”
But generally speaking, if you are just going to copy and paste content from one blog onto your blog network, you're not going to get anywhere.
In fact, Google might even penalize you because there are a lot of scrapers out there.
Unless you have a lot of cash to build such a network, I would not recommend copying and pasting content into your own blog.
There is a solution, though.
If you want original content and you want a lot of it so you can populate your many different blogs, you can use dictablogging or dictation writing.
You just get a microphone, and you find SEO keywords that get traffic. You then outline, very briefly, blog posts based on those target keywords.
Using those 10-20 words on your outline, you can then dictate a piece of content. For every 10 minutes, you produce 1,000 words!
This is how I went from 3,000 words a day, manually writing, all the way to my personal best of 80,000 words per day.