Usually you can. At my university, they just stipulate that they must differ by x number of credits. You also have to be careful if you're going to do three related subjects (i.e., biochem, cell bio, biophysics) because you'll probably end up trying to tripe count certain classes, which they probably won't allow. My advice would be just just make sure you have everything on paper, signed, and registered with the administration before you take a bunch of classes. They can change the requirements pretty quickly without informing you, and I know more than a few people that have been screwed because they didn't have everything on paper beforehand.
All degrees conferred depend on the college/university you attend. There are still universities that will allow a "triple" major, while mine only allows a double at most (and then no minors). Others will allow a major/minor combo, major/minor/minor, major/major/minor... well, you get the idea.
Bottom line: ask your advisor who knows a HECK of a lot more about your school than we do.