May I bring a new, unrelated, business in as a DBA under my existing S Corporation?

Five years ago I established an S Corp where I developed a system for creating recordable gift tags, enclosure cards and florist insert cards. I market them online and through retailers. Prior to catching the entrepreneurial bug, I taught OSHA compliance courses at a university and did some consulting. I would like to return to - and build on - the safety consulting business but with the protection of incorporating. Can I bring it in under my existing corporation as a DBA or must I establish an entirely new S…