I work for a university and our main website is linked/connected to our main Google+ account (as you'd expect.) However, I just got a request from our Alumni group wanting to link their Alumni Google+ page with the main university website. (In the future, I can see other student organizations asking the same). Are there issues with linking more than one G+ account to a website?
You can consider it a profile page. They will gain traffic that's one thing. The win-win situation is that they could add your website on their profile page as well. If you have setup the option to share the content on the social pages, they will gain also awareness on Google and get fast index trough your content. So be careful how and where you add their profile ! All the best, Matt