more than one category. For example, I would be
looking for pages
belonging to category $1 AND category $2 AND category $3).
There is an extension just for that:
https://www.mediawiki.org/wiki/Extension:Multi-Category_Search
DPL does even more of the stuff you want, but does not provide a
search interface.
https://www.mediawiki.org/wiki/Extension:DynamicPageList_%28third-party%29