Humans use their dexterous fingers and adaptable palm in various multiobject grasping strategies to efficiently move multiple objects together in various situations. Advanced manipulation skills, such as finger-to-palm translation and palm-to-finger translation, enhance the dexterity in multiobject grasping. These translational movements allow the fingers to transfer the grasped objects to the palm for storage, enabling the fingers to freely perform various pick-and-place tasks while the palm stores multiple objects. However, conventional grippers, although able to handle multiple objects simultaneously, lack this integrated functionality, which combines the palm's storage with the fingers' precise placement. Here, we introduce a gripper for multiobject grasping that applies translational movements of fingertips to leverage the synergistic use of fingers and the palm for enhanced pick-and-place functionality. The proposed gripper consists of four fingers and an adaptive conveyor palm. The fingers sequentially grasp and transfer objects to the palm, where the objects are stored simultaneously, allowing the gripper to move multiple objects at once. Furthermore, by reversing this process, the fingers retrieve the stored objects and place them one by one in the desired position and orientation. A finger design for simple object translating and a palm design for simultaneous object storing were proposed and validated. In addition, the time efficiency and pick-and-place capabilities of the developed gripper were demonstrated. Our work shows the potential of finger translation to enhance functionality and broaden the applicability of multiobject grasping.