I have a page in the format of
example.com/index.php?ID=someID and my client would like me to 301 permanent redirect some IDs to another domain. Will crawlers only change indexes for the specific ID arguments, or
site.com/index.php in its entirety?
They will do it for specific arguments only. Querystrings are are part of a unique URL. So
example.com/index.php?ID=someID is a completely different URL than
site.com/index.php?ID=someID2 to search engines. They make run off the same code but that means nothing to search engines (or users). So you can redirect some and not others as your business requirements dictate.