Upvote:1
It's hard to prove a negative, but in general nothing stops you from getting a Schengen visa while your Type D visa is being processed. Upon receiving the Type D visa your old Schengen visa will be cancelled to avoid an overlap.
Note that the consulate might not look too kindly on such a practice, as you will potentially overstay your tourist visa if the Type D visa is denied. If you were applying for a work visa, there's also the chance that you will start working before being legally allowed to do so.