Why there so many pitch control surfaces on the Piaggio P180 Avanti?
Surface 1 is a  horizontal stabilizer with elevator, just the same as on any other aircraft with a T tail arrangement.

Surface 2 is called a rear strake or a tail fin. There is one on each side of the fuselage. They provide extra stability during operation at high angles of attack when the fuselage is disturbing the airflow to the vertical tail. They are not movable.

Surface 3 is a canard, providing extra lift. The canards on P.180 have a trailing edge flap. The flap is necessary to counteract the nose down trim of the flaps in the main wing. Without the canard flaps the elevator would not have sufficient authority to maintain adequate pitch control when full flaps are deployed on main wings.

Surfaces 1 and 3 have movable parts, but surface 1 is the only surface connected to pitch axis control of P.180.

Piaggio P.180 article on Flying magazine explaining design features (and a lot more).

Rear strakes- tail fins on Wikipedia