Paginated archives with "show all" link – possible?

Hello,

I have my archives (and search results, categories, etc) set to display a fixed, manageable number of posts, at maximum, using the built-in Settings->Reading->Blog pages show at most setting.

I would like to be able to add a link to the top of these pages that says “show all,” which, when clicked, will take the viewer to a version of that archive/category/tag/search result with no maximum # of posts.

Is this possible? If so, how?

I spent several hours going through google, these forums, and the plugin directory, without finding the answer.