Multi-vehicle cooperative trajectory planning has emerged as a paradigm in connected autonomous vehicles (CAVs) technology research. One of the more common scenarios is cooperative lane-changing trajectory planning within CAVs and platoon coexistence environments. This research introduces a platoon-based cooperative lanechanging (PCLC) control strategy, facilitating a platoon optimally merge into another platoon. The strategy encompasses three dynamic traffic states: micro-platoon formation, lane-changing preparation, and platoon state recovery, which are integral to the lane-changing process. Two transition signals connect these states, enabling the smooth transition between car-following and lane-changing states for CAVs. The PCLC strategy is formulated mathematically through a hybrid model predictive control (MPC) system to achieve multiple objectives, including traffic smoothness, driving comfort, and terminal state reachability. The MPC model is optimized using receding horizon optimization, allowing the system to adapt to the dynamic traffic environment. Furthermore, the stability of the MPC system is proven theoretically. To validate the effectiveness of the proposed strategy, a collaborative simulation platform utilizing Python and SUMO has been established. The results show that (1) compared with the individual cooperative lane-changing (ICLC) strategy, this strategy can improve the lanechanging efficiency by 47.5%. (2) It becomes apparent that a positive speed difference between the subject CAVs and the target platoon will significantly affect the lane changing efficiency. In addition, the execution time is increased more than 30 % when the platoon size is more than 5 vehicles. (3) The application of greater weight to the acceleration penalty weight and the reduction of the vehicle's acceleration limitations can mitigate the speed fluctuations, thereby facilitating a smoother traffic flow. This study integrates CAV platooning control with lane changing control methods to improve lane changing efficiency and reduce traffic fluctuations. The findings of this paper will provide theoretical support for the application of CAV platoons.