I'm not entirely sure of the purpose of what you're trying to achieve.
If you mean having two separate Q2A websites with different questions, you will want to look at the QA_MYSQL_USERS_PREFIX option in qa-config.php. On your second site, set a different table prefix but set the users prefix to the same as the first site. Example here.
If you mean both sharing the same users, questions, everything besides some options it's a bit more difficult. But in theory it could be done with a function override plugin for qa_load_options_results. That function takes the options from the database and sets them into the $qa_options_cache global variable. So in your override you can change whatever options you wish for your second site.