Recent advancements in robotics have led to the integration of flexible robotic arms into everyday applications, serving to assist or replace human operators across a variety of settings due to their safety and adaptability. This paper presents the design, simulation, and empirical evaluation of a two-step expansion flexible gripper, which incorporates inflatable fingers and a pneumatic palm to enhance grasping capabilities. The gripper operates via a pneumatic drive control system activated by a solenoid valve, allowing precise manipulation. This innovative design surpasses existing gripper configurations by facilitating the grasp of objects with diverse geometries and material properties, thereby significantly improving adaptability and functionality. This paper is an extended version of [1].