Is there a way to make a Google+ account work across say 6 different Google email accounts or do you have to to create a new Google+ account for each email account?
Currently (and IMHO unfortunately), the answer is NO. A Google+ account is associated with one, and only one, Google account!
However, at least according to what is written on just-ask-kim.com ("Like Facebook, Google+ has a strict single-account policy"), the alternative that you propose, of creating multiple Google+ accounts, might violate the Google TOS and cause your Google+ account to get banned.
On the other hand, SocialTimes.com, seems to accept as fact that Google's current design "forces users to have multiple profiles on Google+." And this article on iteachithink.com contains a recommendation on how to mitigate this problem.
The "official" Google directive, as explained on Mashable.com, is to use Google Takeout to merge multiple Google+ accounts into a single Google+ account -- ultimately associated with one of your Google accounts.