Almost anything is possible using plugins :) but what you're asking for would be quite difficult. Q2A has an extensive plugin system, so you can certainly set up your own many-to-many table, and add a layer plugin to display appropriate form controls for users to select which answers maps to which questions.
However, showing answers on multiple questions could be tricky. Possibly you could do a core hack in pages/question.php that fetches the appropriate answers and merge/replace the answer array that Q2A fetches.
Actually another strategy that may be simpler is to make a filter or event plugin that, when a new answer is added, automatically adds the answer to multiple questions. Problem here is that the answers are completely separate, so when one is edited the others won't be. But there are ways to handle that too.
Hope that helps!