Overactuated multirotor unmanned aerial vehicles (UAVs) usually consist of multiple tiltable thrust actuators. The controllers are mostly designed by regarding the thrust forces and actuator tilting angles as inputs of outer-loop position and attitude controllers, while formulating an inner-loop controller for each actuator to track the thrust and angle as required by the outer-loop. This hierarchical control strategy separates the complicated combined dynamics into two relatively simple systems, and thus simplifies the control design. However, the interaction between the two systems is neglected and therefore the control performance will be degraded when the inner-loop dynamics are not sufficiently fast. This letter investigates the capability of a new overactuated multirotor UAV configuration, where regular quadcopters are passively hinged onto the frame as tiltable thrust actuators. Apart from the thrust force and tilting angle, each actuator has additional auxiliary torque inputs, which exhibit fast responses as they are not subject to the inner-loop actuator tilting angle dynamics. In this letter, an add-on attitude compensation control is designed exploiting the auxiliary inputs to reduce the tracking and disturbance-rejection errors from the nominal control loop. The effectiveness is demonstrated in simulation and verified by experiment.