Bell 214ST
Under FAA rules, a Student Pilot can fly a Bell 214ST (17,500 lbs. GTOW) VFR, solo. Of course the owner and insurance company might have a problem with that, even if it is legal under the Type Certificate and FARs.
Not all aircraft over 12,500 lbs. require two pilots.
Not all heavy or large aircraft operations require an ATP with Type Rating.
Some pilots (like me, S-58) have Type Ratings on my Commercial license.