Upvote:7
The Schengen system doesn't distinguish between "tourist" and "business" visas for short stays. Once issued, a short-stay Schengen visa is valid for entering and staying in the Shengen area regardless of purpose and itinerary within its validity. (Of course, that's as long as you're not doing something that would be illegal anyway, such as paid work without a permit).
So you don't need a different visa for a tourist visit, as long as you have days and entries left on you visa.
You may have gotten your visa by describing plans for a business visit on a visa application, but since you were granted a multiple-entry visa, this means you're being trusted with further visits to the Schengen area beyond the one you described in your application.