Excluding/Adding Posts to The Loop

I’m developing a custom theme for WP which selectively displays posts during The Loop on the index page.

Currently I’ve set WP to pull 20 posts into The Loop, however it’s not uncommon for only 10 or 15 to display because they don’t match the specific criteria I’ve set up in order for the post to become visible.

I’m wondering if there’s a way to (after The Loop runs) to pull an additional 5 or 10 posts (or however many necessary) into the page’s results in order to display a full 20 posts.

To complicate it more — I’d also like pagination.

Any suggestions before I hack my WP beyond recognition? I’ve searched around the forums but haven’t really found much along these lines.

Thanks for the help.

Cheers, Mike G.