You can legally fly ANY type of helicopter, including turbine (jet) engine-powered helicopters or multi-engine helicopters up to a gross weight of 12,500 lbs. (Only a few VERY LARGE helicopters weigh more than that limit).  The flight controls work the same in EVERY type and size of helicopter.  To safely fly a different size or type of helicopter, however, will usually require some additional training in that aircraft.  Often insurance companies will require a certain number of hours of experience before you can act as solo Pilot-in-Command of different sizes or types of aircraft.