Is it possible to load different versions of the same module? I am running Drupal 6, in a multisite installation. While I fully understand the problems with having varying versions of the same modules running concurrently, I guess I want to know if there's a way to match a specified version of one module to only process requests, or handle calls made by another module? 

I currently have Views 2.x in sites/all/modules. It doesn't work w/ Views Slideshow: Cycle 3.x. I want a way to also have Views 3.x in sites/www.mysite.com/modules, and force it to only process requests that would normally be made by Views Slideshow: Cycle 3.x - but nothing else, as Views 2.x would pick up the rest.

I sort of envision it in the same way Blocks work - where you may have regular expression matching for specified URLS. Thanks for any help in advance.
I'm afraid this simply isn't possible without hacking at Drupal core and the Views module(s) in ways I can't even imagine.

As you know Drupal will only ever let you have one version of a module installed at any one time, and there's no mechanism to 'swap' a module based on a condition (such as the current URL). 

Conceptually this would be almost impossible for quite a lot of reasons; the most obvious that jumps to mind is the fact that one version would have to be uninstalled before the other could be enabled, thus destroying all of the data that exists for the first version. By the time you 'swap' back to the other version, you've lost all of your original Views data.