This paper presents a novel morphing concept for multirotor Unmanned Aerial Vehicles (UAVs) to optimize the vehicle flight performance during multi-parcel deliveries. Abrupt changes in the vehicle weight distribution during a parcel delivery can cause the UAVs to be unbalanced. This is usually compensated by the vehicle flight control system but the motors may need to operate outside their design range which can deteriorate the stability and performance of the system. Morphing the geometry of a conventional multirotor airframe enables the vehicle to continuously re-balanced itself which improves the overall vehicle performance and safety. The paper derives expressions for the static stability of multirotor UAVs and discusses the experimental implementation of the morphing technology on a Y6 tricopter configuration. Flight test results of multi-parcel delivery scenarios demonstrate the capability of the proposed technology to balance the throttle outputs of all rotors.