Use case:
A manager, team lead, etc. needs to find "all tickets that relate to a version". We'll call it Version 1.0.
This means both any ticket that was tagged as "found in version 1.0", OR any ticket that is "planned to be fixed in version 1.0"

Currently this is impossible, because it requires an "OR" concept in the query (affects-version=1.0 OR fix-version=1.0) JIRA lets you do OR within many fields (select multiple) but there is no way to do an OR across two (or more) different fields.

Not sure how something like this would be best represented in the UI. The advanced-search options are already complex enough, so I don't know if you should add anything there.

"OR" searches are sometimes represented in other apps by the metaphor of "stacking" or "joining" searches. Ex. Create Filter A, then create Filter B, then create a filter that is the result of A and B. You could, near the top of the "new filter" UI, give a link "Create combined filter" that takes the user to a simple UI where N number of listboxes are presented each filled with the list of currently-saved filters (and of course the predefined ones too.)

This is somewhat related to JRA-7772, but I don't think it's an exact duplicate.