Short answer: To fly anything commercially you need at least a Commercial Licence. Some things require an ATPL or at least the ATPL theory exams passed.
Slightly longer answer: You don't *need* the ATPL subjects for most piston twins although very few people get a CPL without doing it via the ATPL theory route (instead of the CPL theory route).
As said by others, you could quite happily fly a multi on a PPL. Not in commercial ops though (your specific question). As a PPL you get to pay for the experience. Earning money with a PPL is a no-no.