Pavel Sapehin's post in Complex boolean search: is it possible to use both keywords tag and any? was marked as the answer
Actually, I have found a working solution thankfully to the attached topic. Yep, it is partially possible.
The main idea is to make tags "to_do_1", "to_do_2", etc. a direct children of the tag "to_do". Then I can do the following search:
tag:university tag:to_do* Note: asterisk includes all children tags into the query.