By the way...a1b2c3 -- check with your international advisor also because few years back (06, 07), I know 2 people who did Bachelors twice but were able to get OPT each time. When I asked them they said that if the two degrees are substantially different they can apply for OPT.
This might also depend on each college and how informed are those so called advisors ( some of them are like blank page).
And it makes all sense since OPT is given to have hands-on-experience in the filed of study. If I gradated with biology major and then again with business major; definitely I would need OPT again because my field of study is completely different and I need to gain experience. I know USCIS websites mentions one full term OPT per educational level, But you can always make a case.