You can only do it if the courses that you want to share questions between all belong to the same course category. If so, you can put the questions in the part of the question bank relating to that course category.
Otherwise, the best you can do is probably to arrange the question categories at site level in such a way that it is as easy as possible for different groups of teachers to find the questions they need.
Quiz
What is Context and How a question category relates with a course
Denne diskusjonen har blitt stengt, og du kan derfor ikke svare i den lengre.