The thing is, people like simplicity. If they come to your Facebook page and can't figure out exactly what your business is, they will go somewhere else. That's why I am always amazed at sole traders (who often us the giveaway tag "....and associates") who offer a bewildering range of services, most of which they probably never deliver.
If you want to run a different business, set up a different page and profile. It's easy and it's cheap. By all means link your pages together. Don't offer a smörgåsbord of products unless you're a Swedish delicatessen.