Can I place multiple buttons on a single page that all +1 different URLs?

Yes, but you'll need to edit the button code. Use the href attribute to specify the target URL. For example, if your home page has a module linking to your blog, and you want to add a +1 button to that module, edit the value of the href attribute to point to your blog's URL, like this:

<g:plusone href="http://www.example.com/blog"></g:plusone>