You cant do this with the standard RSS feed, it will only post links from your site to the feed site.

Closest thing Ive found with this is to create a modified hyperlink to the blog feed (s) you want that then open a mini-browsing window for that page as a pop up on top of your current page.

Set it so the pop up does not include an address/search bar and the user can then browse the blog in the window, but has to close it to do anything else, then your site is still open underneath.

It's see more a half way fix though as they could still browse the feed site fully but in a reduced size pop up window but will be forced back to your site to go anywhere else.

Other than that, - custom job.